A native of Brooklyn, New York, Lennart moved to Hollywood, where she was hired to work in the MGM mail room, a job she lost when she attempted to organize a union. She joined the Communist Party in 1939 but left five years later.
Lennart's first script, The Affairs of Martha, an original comedy about the residents of a wealthy community who fear their secrets are about to be revealed in an exposé written by one of their maids, was filmed in 1942 with Spring Byington, Marjorie Main, and Richard Carlson. This was followed in quick succession by A Stranger in Town, Anchors Aweigh, and It Happened in Brooklyn.
In 1947, the House Un-American Activities Committee (HUAC) began an investigation into the motion picture industry. Although she was never blacklisted, Lennart, a former member of the Young Communist League, testified to HUAC in 1952 to avoid being blacklisted. She later regretted this decision.
In 1964, Lennart wrote the book for the Broadway musical Funny Girl, based on the life and career of Fanny Brice and her tempestuous relationship with gambler Nicky Arnstein. It catapulted Barbra Streisand to fame and earned her a Tony Award nomination. In 1968, Lennart wrote the screen adaptation, which won her a Writers Guild of America award for Best Screenplay. It proved to be her last work. Three years later, she was killed in an automobile accident in Hemet, California.
Lennart married actor/writer John Harding in Las Vegas, Nevada in 1945. They had two children, Joshua Lennart Harding (December 27, 1947 - August 4, 1971) and Sarah Elizabeth Harding (born November 24, 1951).