God formed Lilith the first Woman just as he had formed Adam except that he used filth and impure sediment instead of dust or earth. Adam and Lilith never found peace together. She disagreed with him in many matters, and refused to lie beneath him in sexual intercourse, basing Her claim for equality on the fact that each had been created from earth. When Lilith saw that Adam would overpower Her, She uttered the ineffable word of god and flew up into the air of the world. Eventually, She dwelt in a cave in the desert on the shores of the Red Sea. There She engaged in unbridled promiscuity, consorted with lascivious demons, and gave birth to hundreds of Lilim or demonic babies, daily.Adam acted like a spoiled brat, complaining to Yahweh that Lilith would not submit Herself to his, Adam's, every whim and demand. He still wanted sex with Her just as She wanted him, but She required better treatment from him. She would leave Her cave and visit Adam while he slept, "mounting him for Her own pleasure" as the Zohar puts it.
Even when Eve came along, Adam still wanted Lilith, and Lilith still "mounted" him while he slept. To prevent this, Adam wore a thorny bramble around his waist for over 300 years--- I suspect it was to punish Her. Adam didn't much like Eve (and I can harly blame him, being a Lilithian myself!), and I also suspect that his wearing a bramble was to punish Eve.
The problem was that Eve was too much like Adam in that she was made from Adam, while Lilith was his true match and equal (though opposite). The last thing I'd want is a woman who is too much like me. I suspect that Adam realized just how much he lost when he lost Lilith, and wore the bramble as a form of repentance.
--- Shy David