Lily, Frank and Phoebe were in a sexual relationship at the same time Frank got Phoebe pregnant. Consequently, Lily was probably bisexual. Phoebe gave the twins to Lily and Frank to raise and they later married. Frank abandoned them, divorcing Lily who later remarried to a man who went to prison. The man is her widower.
Lily committed suicide by carbon monoxide poisoning when Phoebe and Ursula were around 14. According to Phoebe, she was a drug dealer (Phoebe: "My mother was killed by a drug dealer." Monica: "Your mother killed herself." Phoebe: "She was a drug dealer!").
Phoebe tends to use her mother's suicide to get things like a guy's phone or a blueberry muffin. According to a song written by Phoebe, Lily was subsequently cremated.