Levy was born in New York City in 1935, later attending its City College. He continued on to earn a doctorate in psychology from Michigan State University. Levy was also a trained psychoanalyst, certified by the Menninger Institute for Psychoanalysis in Topeka, KS. Levy later returned to New York and became a clinical psychologist.
In 1965, he directed Sam Shepard's play Red Cross. Two years later he directed Jean-Claude van Italie's America Hurrah. In 1969, Levy directed the off-Broadway erotic revue Oh! Calcutta!, bringing him to the attention of Roger McGuinn of the Byrds, who fancied Levy as librettist for a project inspired by Ibsen's Peer Gynt. The musical stalled, but one song, "Chestnut Mare", co-written by McGuinn and Levy, became one of the Byrds' primary performances.
In the mid-Seventies, Levy met Bob Dylan. Shortly after, the two wrote the song "Isis". Levy also co-wrote six other songs which, along with "Isis", appeared on Dylan's album Desire. These songs included "Hurricane", about the imprisoned boxer Rubin "Hurricane" Carter, and "Joey" about the mafia gangster and hit man, Joey Gallo. In 1975, Levy effectively stage-managed Dylan's Rolling Thunder Revue. Levy's lyrics also entered the repertoires of Joe Cocker, Crystal Gayle, Carly Simon, and McGuinn.
Levy also had several achievements in drama. In 1983 he staged , based on the comic strip Doonesbury, and in 1988 he provided the lyrics for the stage musical of the film Fame. Later came Marat/Sade (1994), Bus Stop (1997), and Brecht on Brecht (2000).
He had two children with his wife Claudia, Maya and Julien.