Of Hungarian ancestry, Lawrence trained as a concert pianist before becoming an actress. She made her first film in 1952 and over the next decade established a following in British films. She graduated to lead roles, but almost exclusively in "B" films.

In 1966 she moved to the United States where she began to appear in films and television, and settled there. By the end of the 1960s her roles began to decrease in frequency and importance, and in 1973 she retired.

She made a brief return in 1975, in the Broadway production of The Constant Nymph, playing the sister of Ingrid Bergman's character.