Lee was born in New York City's Chinatown, to an Indian mother and Chinese father. She started dancing at an early age, and she made her Broadway debut at the age of five as Princess Ying Yawolak in the original production of "The King and I" in 1951. Yul Brynner, the original king, was like a second father to her. After she outgrew the show, she first collected unemployment at age eight. With further dance study in ballet, modern, and afro-Cuban, she appeared in George Balanchine's original production of "The Nutcracker," where she met another idol, ballerina Maria Tallchief, whom she hoped to emulate.