Lilith is from the Midrash, or Jewish legends that the rabbis of the last centuries BCE-first centuries CE told to explain aspects of the Bible with moral lessons. (Other prominent Midrash include the story of Moses getting his Biblical speech impediment by preferring to burn his tongue on hot coal than to worship Egyptian gods).

http://www.jewishencyclopedia.com/articles/9986-lilith

As you can see, there are many different versions of the Lilith story and the modern one that she was Adam's wife, born from the ground like he was and not from his rib, and that she left rather than submit to him, was actually not a popular version originally. Traditionally, Lilith was a demon responsible for child mortality and a succubus who would use sleeping men's semen to produce more demons. The feminist interpretation of Lilith as first feminist popularized by Jewish women today is very modern and downplays the link to infant mortality.

Lilith is supposed to have been the first wife of Adam, who was turned away for basically "wanting to be on top" or otherwise being equal. This doesn't appear in the bible anywhere, so that story may have been made up much later. One source says it is mentioned in Isaiah, so you could check there.

One possible origin for how this entered into Hebrew mythology is from 'Lilitu', a kind of mesopotamian (Babylonian, IIRC) female demon that eats children.

Obviously Lilith isn't an actual historical figure, so there isn't any true origin story, only who said what about her when.

You might get good answers for this question over at /r/AcademicBiblical/ as well.

This question may be worth x-posting to /r/AskReligion