"Lady" was a nickname people used for Holiday; she also released an album entitled "Lady Sings the Blues."
"Corner street societies" can be used to refer to prostitution; Holiday worked as a prostitute for a short while in 1930.
Though she was childless, her mother had her when she was thirteen and was thrown out of her parents' house; this might account for th references to a "baby."
"No Regrets," and "Strange Fruit" are both referenced, as above posters have noted.
Holiday's drug abuse, drinking, abusive relationships, and likely smoking caused her health to deteriorate, and she died young, age 44.
The only truly happy part of her life was the time spent on stage.
Definitely Billie Holiday.
Great song.