Like James, she's dead. Unlike James, she's not an Animagus, and her best friend wasn't (as far as we know) a convicted murderer, which means that there's less about her to talk about.
All we know about her is that she was supposed to be very nice, had dark red hair, green eyes, and saved Harry's life. Unfortunately, her past is not discussed as widely as James', which means she's really quite a minor character.
Hopefully, Rowling will fulfill her promise and talk more widely about Lily in later books. Rowling has revealed that her maiden name is Lily Evans, but in the books she is generally known as Lily Potter. She only appears in the series as a memory.