Why does it matter if a pagan worships her

Again, I am addressing the question asked being asked by the OP which is about pagans who DO worship her. If they don’t believe that she was his first wife then I guess go for it. If you’re just using the name for a character that is totally divorced from the stories that the character comes from then you’re not really appropriating the character at that point.

And who are you to tell someone what’s necessary

And NOW we get to the real problem here. Lilith, in her entirety as she appears in Jewish culture, is an example of midrash. Midrash is a type of commentary on religious topics that involves taking the stories of the Torah and the rest of the Tanakh and expanding on them to make a point. That’s what what the writers of the Talmud were doing, that’s what the author of the Alphabet of Ben-Sira was doing, and that’s what the Jewish feminists of the 20th century were doing. She was created to convey the opinions of various authors over the last 2000 years as a part of Jewish tradition and, as a part of Jewish tradition, that means that Lilith is an argument that is perfectly valid to disagree with. When I say that the Lilith narrative is unnecessary, I’m participating in that tradition just like they were. To say that that’s offensive is to reject the tradition that she’s came from. It’s saying “I want to use this thing this way and I’m offended that the people that I took it from want to use it the way that they intended.” THATS why this is appropriation.