Lehman was born into a wealthy Jewish Long Island family whose fortunes were seriously affected by the Great Depression. Upon his graduation from College of the City of New York (The City College of New York), Lehman became a freelance writer. Lehman felt that freelancing was a "very nervous way to make a living" so he began writing copy for a publicity firm which focused on plays and celebrities. This experience helped form the basis of his 1957 film Sweet Smell of Success, which he co-wrote with Clifford Odets. Lehman wrote many short stories and novellas for magazines like Colliers, Redbook and Cosmopolitan. These attracted the attention of Hollywood and in the mid-1950s Paramount Pictures signed him to a writing contract. His first film, Executive Suite, was a success and he was asked to collaborate on the romantic comedy Sabrina, which also became a hit. Perhaps his most visible contribution to the Hollywood canon is the screenplay of the 1965 mega-hit film version of The Sound of Music.

Perhaps Lehman's most important contribution to Hollywood as a writer was his ingenious screenplay for the 1959 Alfred Hitchcock film, North by Northwest, which starred Cary Grant as a Madison Avenue advertising executive who is mistaken for a government agent by a group of spies including James Mason and Martin Landau.

MGM Studios had actually hired Hitchcock to make a film called The Wreck of the Mary Deare. Collaborating with Lehman, he gave the studio North by Northwest instead. In an audio commentary , Lehman stated that he "wanted to write the Hitchcock picture to end all Hitchcock pictures."

It took him an entire year and several periods of writer's block, as well as a trip to Mount Rushmore to scale the faces of the famous monument. (He got only halfway to the top and bought a camera to give to the park ranger to photograph the famous monument for him.)

North by Northwest was one of Lehman's greatest triumphs in Hollywood and a huge hit for Hitchcock. For his efforts, Lehman received an Academy Award nomination for Best Original Screenplay, as well as a 1960 Edgar Award from the Mystery Writers of America for Best Motion Picture Screenplay.

In addition to screenwriting, Lehman tried his hand at producing, and was among a distinct few in Hollywood who had faith in a film adaptation of Who's Afraid of Virginia Woolf?. He managed to persuade studio executive Jack Warner to allow him to take on the project, and the stark film was a critical sensation, garnering many Academy Award nominations. Lehman was nominated for an Academy Award for 1969's Hello, Dolly! starring Barbra Streisand.

In 1972, Lehman directed his first and last film, Portnoy's Complaint. His 1976 screenplay for Family Plot earned him a second Edgar Award. He basically retired from screenwriting in 1979, aside from some television projects.

In 1977, he published the bestselling novel The French Atlantic Affair, about a group of unemployed, middle-class Americans who hijack a French cruise ship for a $35 million ransom. It was adapted as a TV miniseries in 1979.

Lehman died at UCLA Medical Center after a prolonged illness and was buried at the Westwood Village Memorial Park Cemetery in Los Angeles. He was survived by a wife, Laurie, and his son Jonathan, as well as two sons (Roger and Alan) from his first marriage.