Obviously I do not believe Adam had a wife before Eve. But I do like to speculate on the origins of the whole Lilith mythology. My previous references to her on these blogs have been in the context of her possible connection to Izanami of Japanese mythology.
The fact that the name comes from a Hebrew word for Night leads me to consider that she might be related to other Night goddesses. Like Nyx from Greek mythology, called Nox by the Romans. And Egyptian Mythology has three goddesses who are sometimes defined as night goddesses. Nut, Nebthet, and Kauket. Nut is the wife of Geb who could be argued to be an Adam figure of sorts since his name means earth, and with him the mother of Osiris, Isis, Seth and Nebthet.
I've noticed recently how the name is in a Plural form (the feminine singular would be Lilah), ending with a th is a feminine plural in Hebrew. Lots of feminine Hebrew names end that way without it being significant, possibly just so female names can have variety, so they don't all end with H. But for a mythological context however it may be worth noting. Likewise if you want to speculate it's a code for something.
And also, I can't believe it took so long to occur to me that it might be significant that the one verse that gives the name a Biblical precedent is in a Prophecy about Edom, Isaiah 34 (the "Screech Owl" of the KJV).
Edom is in the Hebrew spelled the same as Adam, but pronounced differently. Edom is the name of a the nation, but also a name for Esau himself, like Israel is for Jacob.
Esau first married at least two Canaanite women, but then because his parents didn't like that, he married a third wife, a daughter of Ishmael. I said at least two, because either these women go by multiple names, or there could be up to 6 wives involved. Genesis 26/28 names them all differently from Genesis 36.
Is it possible the Lilith mythology might have it's origins in the Canaanite wives of Esau feeling displaced by the Ishmaelite?
There has also been a tendency to depict Lilith as having Red Hair, I'm not sure how far back that goes. And Esau has also been associated with Red Hair, since Red is is what Edom, when pronounced that way, means.
In Genesis 36 one of them seems to descend from the Horite clan, which I've speculated elsewhere could be the origin of some of the deities of Egyptian mythology. Thus allowing a possible connection to the Egyptian goddesses I mentioned above.
But it's the connection to Nox that could be interesting to the Edom/Rome connection. The Vulgate of Isaiah 34 translated Lilith as Lamia however, which can be interpreted to mean Nocturnal spirit. Lamia is sometimes in mythology the daughter of Belos/Belus of Egypt, who might be connected to the Hyksos, who might have included Amalekites. Lemures could also be a variation of Lamia.
Coming full circle, the traditional burial place of Izanami of Japanese mythology is in Izumo which is sometimes archaically pronounced Idumo. If the Japanese were partly descended from the lost tribes (and maybe some Edomites came with them) then this could have come from a tradition about Lilith being buried in Edom.