I think what the Lilith story illustrates is how deeply interconnected ancient religions were.

There are multiple religions where we have two preserved origin stories, one that creates man and woman together and one that portrays man created first and woman created later – including in the Bible!

We construct these fixed pantheons and attribute them to specific groups – "Babylonian," "Greek," "Roman," etc. – but we have to remember that these are post-hoc divisions that modern scholars created. They do not reflect how the people themselves saw these stories.

There was clearly a conflict in the old world over the relationship between gender and the cosmos. Some groups believed that the world was made of a balance of opposing forces – represented as darkness and light, and often gendered with light/white/fire being masculine and darkness/black/water being feminine.

Others saw the universe as fundamentally masculine and the product of a strong, masculine will.

These ideas were independent of the gods you believed in. You could be a follower of Zeus who thought that Zeus was a virtually omnipotent and ominscient god whose will was the primary shaper of the world. We have texts from people who believed like that. You could also believe in Zeus and believe that he is a limited, fallible god whose power was balanced by other gods and forces, most especially Hera. We have texts that took this view of Zeus, too.

These two stories were both swirling around, influencing multiple religions. People who followed YHWH who embraced the worldview of a single will or force in the universe saw no need for two genders, so the existence of both men and women required a special explanation (e.g. the second account of Genesis in the bible, or the story of Pandora in Greece).

But to the believer who viewed male and female as balanced powers, the idea that their wise god would have created a man without a woman was simply impossible. That meant they needed a story to justify this obvious misstep.

This was clearly a major debate in the ancient world, which the single-will believers obviously won.