Lawrence was a gay man and was open about his sexuality later in life. He was the longtime companion of Walter David Myden (birth surname Cohn or Cohen). Myden was born in Cooperstown, New York, in 1915 to Jewish parents who had immigrated from the Russian Empire, much like Lawrence's family. He and Lawrence met while serving in the United States Merchant Marines during World War II. Myden was a psychologist and a social worker at a Los Angeles community council. His UCLA dissertation was published in 1957, on the personalities of creative types, such as composers.