So Mr. Whiner, (Adam) gets tired of the animals (yeah, I noticed that too.) and asks God to get her back for him. God, probably sighed and sent out 3 angels to drag Lilith back..... This didn't work and Lilith took off again.
Now things in the reference get a bit weird, Lilith either goes off on a baby killing spree, but promises she won't kill any kids named after the angels who came after her; sleeps with one of the aforementioned angels; has a zillion kids by a bunch of horny demons or makes some kind of sexy deal with the Devil and is transformed into a Demon.
Me, I bet she took off and went looking for a more considerate lover. Eventually Mr. Whiner ("She talked me into trying it!") ends up with the long suffering Eve. Considering Lilith's experience with Adam, I can see why Eve was talking to the only other sentient corporeal life form in the whole garden.
I don't know if Lilith was really bad and deserved to be a demon or she hooked up with one of the angels, but I like that she was not going to put up with being treated badly and took off to make her own way in the world. In my version, Lilith is winged and even though I may call her a demon, I'm very ambivalent about that title. You can decide for yourself if she really is a demon for wanting a little respect.