LEAD: Leonard Bernstein, one of the most prodigally talented and successful musicians in American history, died yesterday evening at his apartment at the Dakota on the Upper West Side of Manhattan. He was 72 years old.

Leonard Bernstein, one of the most prodigally talented and successful musicians in American history, died yesterday evening at his apartment at the Dakota on the Upper West Side of Manhattan. He was 72 years old.

Mr. Bernstein's spokeswoman, Margaret Carson, said he died of a heart attack caused by progressive lung failure.

His death followed by five days the announcement that Mr. Bernstein would retire from performing because of health problems. A heavy smoker for most of his life, he had been suffering from emphysema, pulmonary infections and a pleural tumor.

In recent months, Mr. Bernstein had canceled concerts in Japan and in Charleston, S.C., and a tour of Europe. He conducted his final performance at Tanglewood on Aug. 19, when he led the Boston Symphony in Britten's ''Four Sea Interludes'' and the Beethoven Seventh Symphony.

'Fated for Success'

Long before Mr. Bernstein became, at the age of 40, the youngest music director ever engaged by the New York Philharmonic, the drama critic Harold Clurman sized up the flamboyant musician's future: ''Lenny is hopelessly fated for success.''

It was Mr. Bernstein's fate to be far more than routinely successful, however. His fast-burning energies, his bewildering versatility and his profuse gifts for both music and theater coalesced to make him a high-profile figure in a dozen fields, among them symphonic music, Broadway musicals, the ballet, films and television.

Still, his hydra-headed success did not please all his critics. While he was music director of the Philharmonic from 1959 to 1969, some friends and critics urged him to quit and compose theater music full time. Many regarded him as potentially the savior of the American musical, to which he contributed scores for ''On the Town,''''Wonderful Town,''''Candide'' and ''West Side Story.''

Determining His Focus

At the same time, others were deploring his continued activity in such fields, contending that to be a successful leader of a major orchestra he would have to focus on conducting.

Still other observers of the Bernstein phenomenon wished he would concentrate on the ballet, for which he had shown an affinity (''Fancy Free,''''Facsimile''), or on opera and operetta (''Trouble in Tahiti,''''Candide'').

Or on musical education. His television programs on such subjects as conducting, symphonic music and jazz fascinated millions when he appeared on ''Omnibus,'' the cultural series, and later as star of the Philharmonic's televised Young People's Concerts.

And still others, a loyal few, counseled Mr. Bernstein to throw it all over and compose more serious symphonic scores. His gifts along this line were apparent in such works as his Symphony No. 1 (''Jeremiah'') of 1942, Symphony No. 2 (''The Age of Anxiety'') of 1949 and Symphony No. 3 (''Kaddish'') of 1963. He played the piano well enough to have made a separate career as a virtuoso. He was a facile poet. He wrote several books, including the popular ''The Joy of Music'' (1959). He was a teacher of rare communicative talent, as television audiences discovered.

But Mr. Bernstein resolutely resisted pressure to restrict his activities. During his decade as the Philharmonic's musical director, he grew steadily as an interpreter and as a technician.

His performances of Mahler's symphonies were almost universally conceded to be of the highest quality, and his recordings for Columbia Records of the complete set not only constituted the first such integral collection but also continue to be regarded as among the most idiomatic Mahler performances available. His obsession with that composer, in fact, has been credited with generating the Mahler boom in America.

His conducting of works by Classical composers like Mozart and Haydn, often derided in his earlier days, attracted more and more praise as his career unfolded and he could relax a little. ''There is nothing Lenny can't do supremely well,'' an acquaintance remarked several years ago, ''if he doesn't try too hard.''

The future Renaissance man of American music was born in Lawrence, Mass., on Aug. 25, 1918, the son of Samuel and Jennie Resnick Bernstein. His father, a beauty-supplies jobber who had come to the United States from Russia as a boy, wanted Leonard to take over the business when he grew up. For many years the father resisted his son's intention to be a musician.

The stories of how he discovered music became encrusted with legend over the years, but all sources agree he was a prodigy. Mr. Bernstein's own version was that when he was 10 years old his Aunt Clara, who was in the middle of divorce proceedings, sent her upright piano to the Bernstein home to be stored. The child looked at it, hit the keys and cried: ''Ma, I want lessons!''

Until he was 16, by his own testimony, he had never heard a live symphony orchestra, a late start for any musician, let alone a future musical director of the Philharmonic. Virgil Thomson, while music critic of The New York Herald Tribune in the 1940's, commented on this:

''Whether Bernstein will become in time a traditional conductor or a highly personal one is not easy to prophesy. He is a consecrated character, and his culture is considerable. It might just come about, though, that, having to learn the classic repertory the hard way, which is to say after 15, he would throw his cultural beginnings away and build toward success on a sheer talent for animation and personal projection. I must say he worries us all a little bit.'' These themes - the concern over Mr. Bernstein's ''talent for animation'' and over his penchant for ''personal projection'' - were to haunt the musician through much of his career.

Economy of Motion Not His Virtue

As for ''animation,'' that theme tended to dominate much of the criticism of Mr. Bernstein as a conductor, particularly in his youthful days. Although he studied conducting in Philadelphia at the Curtis Institute with Fritz Reiner, whose precise but tiny beat was a trademark of his work, Mr. Bernstein's own exuberant podium style seemed modeled more on that of Serge Koussevitzky, the Boston Symphony's music director. The neophyte maestro churned his arms about in accordance with some inner message, largely ignoring the clear semaphoric techniques described in textbooks. Often, in moments of excitement, he would leave the podium entirely, rising like a rocket, arms flung aloft in indication of triumphal climax.

So animated, in fact, was Mr. Bernstein's conducting style at this point in his career that it could cause problems. At his first rehearsal for a guest appearance with the St. Louis Symphony, his initial downbeat so startled the musicians that they simply looked in amazement and made no sound.

Like another prodigally gifted American artist, George Gershwin, Mr. Bernstein divided his affections between the ''serious'' European tradition of concert music and the ''popular'' American brand. Like Gershwin, he was at home in jazz, boogie-woogie and the cliches of Tin Pan Alley, but he far outstripped his predecessor in general musical culture.

In many aspects of his life and career, Mr. Bernstein was an embracer of diversity. The son of Jewish immigrants, he retained a lifelong respect for Hebrew and Jewish culture. His ''Jeremiah'' and ''Kaddish'' symphonies and several other works were founded on the Old Testament. But he also acquired a deep respect for Roman Catholicism, which was reflected in his ''Mass,'' the 1971 work he wrote for the opening of the John F. Kennedy Center for the Performing Arts in Washington.

A similar catholicity was reflected throughout his music. His choral compositions include not only songs in Hebrew but also ''Harvard Songs: Dedication and Lonely Men of Harvard.'' He was graduated in 1939 from Harvard, where he had studied composition with Walter Piston and Edward Burlingame Hill.

A sense of his origins, however, remained strong. Koussevitzky proclaimed him a genius and probable future musical director of the Boston Symphony - ''The boy is a new Koussevitzky, a reincarnation!'' - but the older conductor urged Mr. Bernstein to improve his chances for success by changing his name. The young musician replied: ''I'll do it as Bernstein or not at all!''

He pronounced the name in the German way, as BERN-stine, and could no more abide the pronounciation BERN-steen than he could enjoy being called ''Lenny'' by casual acquaintances.

In a sense, he was in lifelong flight from Lenny Bernstein, from being treated as the raffish ''ordinary guy'' that the nickname seemed to suggest. Although some elder members of the New York Philharmonic never stopped calling him Lenny, Mr. Bernstein lived down the nickname, and in his late years heard himself addressed almost reverentially as ''Maestro'' in the world's music capitals. The man who had been patronized in print for many years as ''Glamourpuss'' or ''Wunderkind of the Western World'' became a favorite of Vienna both as conductor and as accompanist for such lieder specialists as Dietrich Fischer-Dieskau and Christa Ludwig.

Fame brought the usual honorary degrees, and honors far beyond the usual. He not only conducted at La Scala in Milan, at the Metropolitan Opera and at the Staatsoper in Vienna, but he was also invited by Harvard in 1973 to lecture, as Charles Eliot Norton Professor of History, on linguistics as applied to musical analysis. The distinction had previously been conferred on Robert Frost, T. S. Eliot, Igor Stravinsky, Aaron Copland and Paul Hindemith. Typically, Mr. Bernstein's Harvard performance was greeted with a mingling of critical raves and boos.

Harvard played an important part in Mr. Bernstein's rise, providing a pinch of Brahminism. The boy whose bar mitzvah was at Temple Mishkan Tefila had gone on to the elite Boston Latin School, and graduated cum laude from Harvard with a B.A.

During his last semester at Harvard, he organized and led a performance of Marc Blitzstein's ''Cradle Will Rock,'' a left-wing musical that had been banned in Massachusetts, but that could not be proscribed within the academic walls. It was not his first fling as a producer. At age 16 he had starred in his own production of ''Carmen'' at a summer camp, playing the title role alluringly in wig and black gown.

It was as a result of another schoolboy production, at Camp Onota in the Berkshires, that he met Adolph Green, with whom he later collaborated in several Broadway musicals. Mr. Bernstein was a camp counselor and theater director and Mr. Green was in ''The Pirates of Penzance.''

An Unlikely Start For a Conductor

Subsequently, when Mr. Bernstein was out of a job in New York City, he looked up Mr. Green, moved in with him in his East Ninth Street apartment in Greenwich Village, and began playing the piano at the Village Vanguard for a group called the Revuers. The ensemble included, besides Mr. Green, his musical comedy collaborator Betty Comden and the actress Judy Holliday.

Mr. Bernstein met Aaron Copland at Harvard in 1937, and through him came to know two other aspiring composers, Roy Harris and William Schuman. Admiring his intuitive grasp of modern music and his phenomenal skill at playing complex orchestral scores on the piano, the composers agreed that Mr. Bernstein should become a conductor. Dimitri Mitropoulos, the New York Philharmonic's music director, met Mr. Bernstein in 1938 and added to the consensus.

At that point, Mr. Bernstein ''didn't know a baton from a tree trunk,'' as he later put it.

Nevertheless, he had made up his mind. Because he had applied at the wrong time of the year and was turned down by the Juilliard School, he went to Philadelphia to audition for Reiner's conducting class at the Curtis Institute. The Hungarian maestro opened a score in the middle, put it on the piano and told Mr. Bernstein to play until he could recognize the piece.

The aspiring conductor, who was having difficulty seeing the music because he was suffering from an allergic reaction to Copland's cat, nevertheless discerned that the work was the ''Academic Festival'' Overture of Brahms. He was accepted.

At Curtis, he studied conducting with Reiner and piano with Isabella Vengerova. His earlier piano teachers included a neighbor, Freida Karp, Helen Coates and Heinrich Gebhard. In 1940 he went to Tanglewood, where he studied at the Berkshire Music Center with Koussevitzky, who quickly adopted Mr. Bernstein and called him Lenyushka.

In later years, Mr. Bernstein prided himself on having retained the respect and friendship of both Koussevitzky and Reiner, who held virtually opposing ideas about what a conductor should do and how he should do it. But the story as the famously irascible Reiner told it to acquaintances was different: ''He didn't leave me for Koussevitzky - I threw him out.''

In truth, not all of Mr. Bernstein's associations with elder colleagues were warm and collegial. In John Gruen's biographical ''The Private World of Leonard Bernstein,'' published in 1968, Mr. Bernstein asserted that Artur Rodzinski had once pinned him against the wall of a dressing room, trying to choke him because of jealousy over the young assistant's flair for publicity. But according to Mr. Bernstein, Rodzinski had by this time become somewhat peculiar: he always carried a gun in his back pocket, for instance, for psychological support when he faced the orchestra.

A Boycott Causes Stumble at the Start

It was Rodzinski, however, who gave Mr. Bernstein his chance at conducting the New York Philharmonic at a lean time when the young man was scraping along as a musician in New York. When he was 22, Mr. Bernstein had been offered a guest-conducting engagement with the Boston Symphony by Koussevitzky but had been forced to refuse. The American Federation of Musicians, to which Mr. Bernstein belonged, advised its members to boycott the Boston Symphony, the last of the major orchestras remaining unorganized. Mr. Bernstein tried to mark time by opening a teaching studio in Boston, he later recalled, but ''nobody came.''

That fall, he moved to New York, where he fared hardly better.

Eventually he got a $25-a-week job at Harms-Remick, a music-publishing house, where his duties included listening to Coleman Hawkins and Earl (Fatha) Hines, and getting their jazz down on paper. He also wrote popular arrangements under the name of Lenny Amber (Bernstein in English).

The Philharmonic offer by Rodzinski came without warning. Rodzinski had heard Mr. Bernstein conduct a rehearsal at Tanglewood, remembered the young man, and after an hour's discussion, had hired him as an assistant for the 1943-44 season.

Assistant conductors by tradition do a great deal of assisting, but not much conducting. Destiny had other plans for Leonard Bernstein, however, and when opportunity knocked one Sunday afternoon in 1943, he was ready to open the door. On Nov. 14, Bruno Walter fell ill and could not conduct the Philharmonic. The young assistant took over his program (works by Schumann, Rosza, Strauss and Wagner) and achieved a sensational success. Because the concert was broadcast over radio and a review appeared on page 1 of The New York Times the next day, the name of Leonard Bernstein suddenly became known throughout the country.

''Typical Lenny luck,'' some longtime Bernstein observers said. But Mr. Bernstein had given luck a hand: Knowing that Walter was not feeling well, he had studied the program's scores especially hard, just in case. At 25, he had become a somebody in the symphonic world.

After that break, though he was still more then a decade away from becoming music director of the Philharmonic, Mr. Bernstein began to consolidate his gains. He put in three exciting but financially unproductive seasons (1945-48) as conductor of the New York City Symphony. He received no fee, and neither did the soloists.

In 40's, Celebrity And Back Muscles

In the late 1940's Mr. Bernstein bloomed as a public figure. He came to be a familiar sight at the Russian Tea Room, at Lindy's and at Reuben's. Columnists reported that he liked boogie-woogie, the rumba and the conga, and that female admirers swooned when he stepped on the podium.

Tallulah Bankhead once watched Mr. Bernstein conduct a Tanglewood rehearsal and said to him in her husky baritone: ''Darling, I have gone mad over your back muscles. You must come and have dinner with me.''

Just about everyone in those years wanted Mr. Bernstein. The United States Chamber of Commerce named him as one of the outstanding men of the year, along with Nelson A. Rockefeller and John Hersey. His fans, it was reported, ripped at his clothes and attacked him in his car. Paramount tested him for the title part in a film about Tchaikovsky, but he was turned down, according to the conductor, because ''my ears were too big.''

Mr. Bernstein, in fact, looked the part of a pop idol with his strong profile and wavy black hair.

Musically, his career was on the upswing, too. In 1947 he conducted a complete Boston Symphony concert as a guest, the first time in Koussevitzky's 22-year reign that any other conductor had been permitted to do that in Carnegie Hall. He served as musical adviser of the Israel Philharmonic Symphonic Orchestra for the 1948-49 season. He was a member of the Berkshire Music Center from 1948 and head of its conducting department from 1951. He served as professor of music at Brandeis University from 1951 to 1956.

In 1953 Mr. Bernstein became the first American-born conductor to be engaged by La Scala in Milan, Italy's foremost opera house, leading a performance of Cherubini's ''Medea'' with Maria Callas in the title role.

During the six-year tenure of Mitropoulos as music director of the Philharmonic, beginning in the 1951-52 season, Mr. Bernstein was a frequent guest conductor. In 1957-58, the two worked jointly as principal conductors of the orchestra. A year later, Mr. Bernstein was named music director.

The New York appointment would have been a severe test of any conductor. The orchestra's quality had gone downhill, its repertory had stagnated and audiences had fallen off. Orchestra morale was low and still sinking. Mr. Bernstein leaped in with his customary brio and showmanship and his willingness to try new ideas.

He designated the Thursday evening concerts as ''Previews,'' at which he spoke informally to the audience about the music. He built his season around themes like ''Schumann and the Romantic Movement'' and ''Keys to the 20th Century.'' Strange-sounding works by avant-garde composers like Elliott Carter, Milton Babbitt, Karlheinz Stockhausen, Gunther Schuller and John Cage began to infiltrate the Philharmonic's programs. He took the orchestra on tours to Latin America, Europe, Japan, Alaska and Canada.

It sometimes seemed that Mr. Bernstein could not possibly squeeze in one more engagement, one more social appearance. During one particularly busy stretch, he conducted 25 concerts in 28 days. His conducting style accurately reflected his breathless race through life. Although in later years he toned down his choreographic manner, he remained one of the more consistently elevating conductors of his time. That irrepressible buoyancy sometimes led to trouble: in 1982 he fell off the stand in Houston while conducting Tchaikovsky and two years later encored that frightening stunt while leading the Vienna Philharmonic in Chicago. The worst injury he suffered, however, was a bruise from a medallion he wore around his neck.

Throughout his Philharmonic years, he kept his ties with Broadway and the show-business friends he had made before he became an internationally adulated maestro. He had already written music for the musical version of ''Peter Pan'' (1950) and ''The Lark,'' a play starring Julie Harris (1955). For Hollywood, he wrote the score to ''On the Waterfront'' (1954). Musical successes on the stage followed: ''On the Town'' (1944), ''Wonderful Town'' (1953), ''Candide'' (1956) and ''West Side Story'' (1957). Several of the stage works continue to thrive: in 1985 Mr. Bernstein conducted a quasi-operatic version of ''West Side Story'' (the cast included Kiri Te Kanawa and Jose Carreras) that pleased him immensely and introduced the work to a new generation of listeners.

Then there were the ballets ''Fancy Free'' (1944) and ''Facsimile'' (1946); the song cycles ''I Hate Music'' and ''La Bonne Cuisine''; the ''Jeremiah'' and ''Age of Anxiety'' symphonies; the one-act opera ''Trouble in Tahiti''; Serenade for violin and string orchestra with percussion; the Symphony No. 3 (''Kaddish''), and the ''Chichester Psalms.''

In the years after he had left the music directorship of the Philharmonic to become the orchestra's laureate conductor, he returned to the theater. He created the ecumenical and controversial ''Mass'' and, with Jerome Robbins, the ballet ''Dybbuk,'' staged by the New York City Ballet in 1974.

Mr. Bernstein's life took a turn toward greater stability in 1951 when he married the actress Felicia Montealegre Cohn. Her American father had been head of the American Smelting and Refining Company in Chile and she had been sent to New York City to study the piano. After several years of off-and-on romance, they were married in Boston. They had three children: a daughter, Jamie, a son, Alexander Serge (named for Serge Koussevitzky) and a second daughter, Nina.

In addition to his children, who all live in New York City, and his mother, of Brookline, Mass., Mr. Bernstein is survived by a sister, Shirley Bernstein of New York City, and a brother, Burton, of Bridgewater, Conn.

Mr. Bernstein and his wife began a ''trial separation'' after 25 years of marriage. They continued, however, to appear together in concerts, one such occasion being a program in tribute to Alice Tully at Alice Tully Hall, where Mr. Bernstein conducted Sir William Walton's ''Facade'' with his wife as one of the two narrators. Mrs. Bernstein died in 1978 after a long illness.

After leaving the music director's post with the Philharmonic in 1969, Mr. Bernstein hardly curtailed his frantic activities. He continued to guest-conduct, to record for Columbia Records, to conduct at the Metropolitan Opera and to play the piano for lieder recitalists. His company, Amberson Productions, which he had formed with his friend Schuyler G. Chapin to handle his diverse interests, expanded into the new field of videocassettes.

Mr. Bernstein, a longtime Democrat and liberal, took a deep interest in politics and was a friend of the Kennedys. His ''Mass'' was dedicated to John F. Kennedy. Among guests at fund-raising parties in his apartment during the late 1960's, one could find some of the leading civil-rights advocates of the period, a form of hospitality that inspired the writer Tom Wolfe to coin the term ''radical chic.'' In his book ''Radical Chic & Mau-Mauing the Flak Catchers,'' Mr. Wolfe described a fund-raising party that Mr. Bernstein gave for the Black Panthers.

During Mr. Bernstein's Philharmonic decade, the orchestra engaged its first black member, the violinist Sanford Allen.

He continued composing, if only in spurts. Late works included ''Jubilee Games,''''Arias and Barcarolles,''''Halil'' and a sequel to his opera ''Trouble in Tahiti'' entitled ''A Quiet Place.'' After its premiere in Houston in 1983, ''A Quiet Place'' was produced at the Vienna State Opera, La Scala and the Kennedy Center in Washington.

Almost to the time of his death, Mr. Bernstein carried on a bewildering variety of activities, rushing about the world with the same tireless abandon that had characterized his life in the days when he was churning out a hit a season on Broadway.

But Broadway had changed by the time Mr. Bernstein's final theatrical score reached the Mark Hellinger Theater in March 1976. The long-awaited work that he and Alan Jay Lerner had composed, ''1600 Pennsylvania Avenue,'' closed after seven performances.

He turned up in Israel, where the Israel Philharmonic was putting on a Leonard Bernstein retrospective festival to celebrate the 30th anniversary of his debut on an Israeli podium. During a two-week period, his music was heard in concert halls, theaters, movie houses and other auditoriums all over the country. In 1988, when he was 70 years old, Mr. Bernstein was named laureate conductor of the Israeli orchestra. That birthday year brought honors from all directions, but none seemed to gratify him more than the celebration staged for him at the Tanglewood Festival, scene of so many triumphs early in his career. On Nov. 14, 1988, to mark the 45th anniversary of his Philharmonic conducting debut, he led the orchestra in an all-Bernstein concert.

Laurel wreaths continued to shower on him in his last decades. Elected to the American Academy and Institute of Arts and Letters in 1982, he was awarded the Academy's Gold Medal three years later. The city of Milan, home of La Scala, also gave him its Gold Medal.

A discordant note sounded in 1989 when he refused to accept a medal from the Bush Administration, apparently as a protest against what he regarded as censorship of an AIDS exhibition by the National Endowment for the Arts. Like many other artists and public figures, he contributed his services at concerts to benefit the fight against AIDS.

Mr. Bernstein's private life, long the subject of rumors in the musical world, became an open book in 1987 when his homosexuality was brought to wide public attention by Joan Peyser's ''Bernstein: A Biography.''

As Age Advances, The Pace Does Too

Far from slowing down as age encroached, Mr. Bernstein seemed to accelerate. Last Christmas he led a performance of Beethoven's Ninth Symphony in Berlin to celebrate the crumbling of the wall between East and West Germany. With typical flair, he substituted the word ''Freiheit'' (''Freedom'') for the poet's ''Freude'' (''Joy'') in the choral finale. The East German Government bestowed on him its Star of People's Friendship Medal.

Although he had reportedly refused an offer to return to the New York Philharmonic as music director, he was scheduled to conduct six weeks of concerts for the next few seasons. Before collapsing from exhaustion this year in Japan, Mr. Bernstein had taken part in the Pacific Music Festival.

Late in his extraordinarily restless and fruitful life, Mr. Bernstein defended his early decision to spread himself over as many fields of endeavor as he could master. ''I don't want to spend my life, as Toscanini did, studying and restudying the same 50 pieces of music,'' he wrote in The Times.

''It would,'' he continued, ''bore me to death. I want to conduct. I want to play the piano. I want to write for Hollywood. I want to write symphonic music. I want to keep on trying to be, in the full sense of that wonderful word, a musician. I also want to teach. I want to write books and poetry. And I think I can still do justice to them all.''

Photos: Leonard Bernstein (Steve J. Sherman, 1988) (pg. A1); Leonard Bernstein conducting the New York Philharmonic during his farewell concert as he retired as music director in 1969. (Michael Evans/The New York Times); Mr. Bernstein at the keyboard in 1945. (Graphic House); Leonard Bernstein instructing singers from the cast of ''West Side Story'' in 1957. At the piano was Stephen Sondheim, who was co-lyricist. (Friedman-Abeles) (pg. B6)