Came waaaaaaaaaay after A & E, see Isaiah 34:14. Babylonian Talmud and the Alphabet of Ben Sira 'flesh out' what 'lilith' is/was, but they refer to 'it' as some type of animal, the incarnation of 'night', or, a demon responsible for 'wet dreams'........
depends on the source Lilith was/is adams first wife and was cast out of paradise for dominating him.
That version makes for a better story no.