[1] Born Joseph Lichtman in Brooklyn, Layton began his career as a dancer in Wonderful Town (1953), and he appeared uncredited in the ensemble cast of the original live TV production of Rodgers and Hammerstein's Cinderella (1957) starring Julie Andrews.

In addition to his many legitimate theatre credits, he conceived and directed Broadway concerts for Bette Midler (1975), Diana Ross (1976), Cher (1979), and Harry Connick Jr. (1990).

He also directed and/or produced specials for Paul Lynde, Hal Linden, Richard Pryor, and Olivia Newton-John.

In 1984, Layton was one of the three choreographers credited with staging the dances for the Opening ("How the West Was Won" sequence) and Closing (the break-dances in "All Night Long") ceremonies of the 23rd Summer Olympiad of Los Angeles.

In 1985, Layton directed and choreographed a Michael Edgley revival production of Aloha: A Musical of the Islands by Eaton "Bob" Magoon[5][6][7] and Sir Robert Helpmann at His Majesty's Theatre, Auckland,[8] Auckland (New Zealand), starring Derek Metzger from the Hamilton world première production,[9][10][11] with Hollywood actress Patricia Morison.