"Stormy Weather" was Lena Horne's signature song as well as a chillingly apt metaphor for her career. Long celebrated for her striking beauty and silky voice, she overcame profound racism on her way to becoming one of the best-known African American performers in the country. At MGM, she had a seven-year contract in the 1940s when no other African American had such long-term deals. But her movie scenes were filmed so they could be easily excised for release in the Jim Crow South. As a singer in the 1950s, Horne often performed for white audiences in supper clubs then cursed...