This subject came up in the other thread over here, and we have read some interesting studies on the subject.
This is a link to one article that asks some relevant questions about the doctrine. Please feel free to post others.
So let's assume that this story is true. God created Adam and Lilith and the rest of mankind in genisis 1. Then Lilith rebeled and became Isaiah 14;12, or something like that. God then placed Adam in the Garden in Genisis 2 and created Eve from Adam.
That would explain the Adam and Eve story about the apple as being about sexual desire, ultimately coming from Lilith. Satan, taught by Lilith taught Eve about sex, who then taught Adam, which came the curse of mankind. Cain was from Satan. Abel from Adam. And the two blood lines have been at war ever since. If man was created in Genisis 1 separate from Adam then that explains where Cain got his wife.
This is a link to one article that asks some relevant questions about the doctrine. Please feel free to post others.