Lee was born Norma Engstrom. After singing on local radio, she became famous as a vocalist with Benny Goodman's band. As a solo artist she became a top nightclub, TV, and recording star. She played dramatic leads in two films and appeared as a singer in two others; she also did voice-over singing and acting for the Disney feature cartoon Lady and the Tramp (1955). For her performance in Pete Kelly's Blues (1955) she received a Best Supporting Actress Oscar nomination. She wrote the lyrics for many of her songs and for three films. She married and divorced actors Brad Dexter and Dewey Martin.