whats lily and rufuses history?

It's kind of confusing, but they were together when they were younger, and Lily was a groupie for Rufus' band. Lily got pregnant, she never told Rufus because her mom forced her to choose between her inheritance and Rufus, and she took the money. So then she had their baby while she was attending Brown, but she had it in a hospital in France and gave the child to an adoption agency in Boston (I don't understand how she was at Brown/France/Boston at the same time tbh). Then they both married other people and had kids, but once Dan and Serena meet, they saw each other more often. Rufus' wife cheated and they got divorced, and they were kinda, but not really, together. Then Lily married Bart, he died and they've been whatever since.