What if a semi-monotheist religion emerges around Lilith or Anat goddess with a complex theology and becomes influential in the Middle-East ?
This is a pretty broad question. Why do you think that a monotheistic religion venerating a war goddess would be all that different from one venerating a sky god, considering that the early Hebrews were also pretty conquer-y (or at least, tried a lot).
It's worth noting that Lilith seems to always have been some sort of demon, rather than a goddess, even in ancient Mesopotamia.
Because people reacting to the excesses of patriarchal Judaism (and hence the other Abrahamic religions) go overboard when they find traces of a 'Lilith' figure buried deep in Hebrew history, and figure she must be everything right that they despise about patriarchal OTL Judaism?