Elliot Lawrence, who led a musically adventurous big band in the 1940s and ’50s, and then had a long career on Broadway and in Hollywood, including more than 40 years leading the orchestra at the annual Tony Awards show, died July 2 at a hospital in New York City. He was 96.

A son, musician and composer Jamie Lawrence, confirmed the death but did not cite a specific cause.

Mr. Lawrence, who began playing piano at 3, formed his first band at 12. Beginning in 1945, Mr. Lawrence was the leader of the house band of Philadelphia’s WCAU radio, where his parents were longtime fixtures.

With many groups disbanding during World War II because musicians were being drafted, Mr. Lawrence filled the gap and was heard on nationwide radio broadcasts before he turned 21. (He was exempt from military service because of severe asthma.)

After the war, he moved to New York, reorganizing his band into a forward-thinking ensemble that combined the modern jazz sounds of bebop with elements of classical music: It was almost certainly the only jazz orchestra with an oboe, bassoon and French horn.

Mr. Lawrence may not have had as large a following as other bandleaders, such as Woody Herman and Count Basie, but he recorded a number of well-received albums, toured the country and fostered the careers of many prominent musicians and arrangers, including Gerry Mulligan, Al Cohn, Red Rodney and Johnny Mandel. The band Mr. Lawrence fronted from about 1949 to 1951 was called the Elevation band after a boppish tune he and Mulligan wrote, which became a minor jazz classic.

“His big band recordings of the late 1940s and 1950s had superb post-war optimism and freshness, especially when playing Gerry Mulligan arrangements,” jazz critic Marc Myers wrote in an appreciation of Mr. Lawrence on the JazzWax website. “His bands were always tight, well rehearsed and loaded with the best musicians.”

He broke up his touring band in 1956, when it became financially untenable because of the rise of rock-and-roll. Another reason, Mr. Lawrence told the Pennsylvania Gazette, a University of Pennsylvania alumni magazine, was that one of his musicians approached him and said, “El, I’m sorry to tell you this, but out of the 16 guys in the band, 14 of them are junkies.”

Since the early 1950s, Mr. Lawrence had worked for CBS as a bandleader and conductor for various radio and television productions. In 1959, he accompanied “The Ed Sullivan Show” to Moscow for one of the first entertainment programs broadcast from the Soviet Union. On the trip, Mr. Lawrence met Marge and Gower Champion, who were acclaimed Broadway dancers and choreographers.

“During the tour,” Mr. Lawrence recalled in 2009 to the Pennsylvania Gazette, “Gower came to me and said, ‘You’ll do TV the rest of your life and no one will know who you are. Why don’t you come back with me and do my next show?’ That’s how I got the gig as music director for ‘Bye Bye Birdie.’ ”

He received a Tony nomination for his work on the hit musical and then in 1961 moved on to “How to Succeed in Show Business Without Really Trying,” with music and lyrics by Frank Loesser. Mr. Lawrence won a Tony Award for best conductor and musical director for “How to Succeed in Business,” which ran on Broadway for more than three years.

While working in television, Mr. Lawrence won multiple Emmy Awards and was the conductor and arranger for musical specials featuring performers such as Plácido Domingo, Patti LaBelle, Anita Baker, Ann-Margret, Joel Grey, Burt Bacharach and Dionne Warwick.

Mr. Lawrence won his last Emmy Award in 2013, in his 46th and final year as music director of the Tony Awards. He also directed the musical portions of the Kennedy Center Honors several times between 1993 and 2005.

Mr. Lawrence wrote the music for many soap operas, composed the score for the 1976 film “Network” and the opening sequence of “The French Connection” (1971). He was a longtime musical producer for the N.W. Ayer advertising company in Philadelphia.

Elliot Lawrence Broza was born Feb. 14, 1925, in Philadelphia. His father, Stan Lee Broza, helped found WCAU radio in Philadelphia, and his mother, Esther Broza, wrote for radio. In 1927, his parents started a children’s variety show, “The Horn and Hardart Children’s Hour,” which ran on radio and later on television until 1958.

Elliot Broza made his musical debut at 3 on his parents’ radio show. He later contracted polio and, while living with his grandparents in Atlantic City, did exercises to regain the strength in his hands. At 12, he founded his first group, the Band Busters, which played on radio and at dances and included 14-year-old clarinet virtuoso Buddy DeFranco, who became a major jazz star.

After studying classical piano throughout his youth, Mr. Lawrence entered the University of Pennsylvania at 16. As the student director of the marching band, he recruited musicians from nearby military units to fill its ranks and then arranged Penn fight songs in the popular swing-music style of the time.

“So here we come, marching onto Franklin Field to a drum cadence, all the guys in different uniforms,” he told the Pennsylvania Gazette. “They were required to wear the uniform of their own service. And a roar went up in the crowd. We stopped at the goal post, and went through a medley of five minutes of all the Penn tunes in a swing version. It was a big hit.”

Mr. Lawrence, who dropped his last name because he didn’t want to cash in on his parents’ broadcasting fame, was 19 when he graduated with honors from Penn in 1944.

His wife of 63 years, the former Amy Bunim, died in 2017. Survivors include four children, Danny Lawrence and Jamie Lawrence, both of New York, Alexandra Lawrence of New Haven, Conn., and Mia Lawrence of Katonah, N.Y.; and five grandchildren.

Several of Mr. Lawrence’s recordings from the 1950s, including “Swinging at the Steel Pier,” “Jazz Goes Broadway” and “Elliot Lawrence Plays Gerry Mulligan Arrangements,” have been re­released in recent years.

Mr. Lawrence said his encyclopedic knowledge of different forms of music began at an early age.

“When I was 10, my chore was to accompany my mother on the piano in our living room,” he told Myers in 2015. “As a result, I played the entire American Songbook by age 12. This came in handy whenever my parents threw a party. My job was to sit there all night until I was bleary-eyed accompanying the gang.”