Lydia Rapoport was born in 1923 in Vienna, Austria, to an intellectual Jewish family. Her family emigrated to New York City when she was a child. She graduated from Hunter College in 1942 and went on to the Smith College School for Social Work. She received her Master's in Social Work in 1944 at the age of twenty-one, making her the youngest degree recipient in the School's history.

In the course of her career, Rapoport conducted consultations, workshops, and seminars at various institutions, among them Hebrew University in Israel from 1963 to 1964, the Smith College School for Social Work in 1965, 1966 and 1967, and the University of Chicago in 1968. She served on the faculty of the University of California at Berkeley from 1956 until her death on September 6, 1971. In 1974, the Lydia Rapoport Distinguished Visiting Professorship and Lecture Series was established in her memory at the Smith College School for Social Work.