None of these claims are backed up by actual scholarly or theological evidence. It was briefly theorized that Lilitu and Lilith may have links but the actual research shows this was debunked decades ago. Lilith is a figure from Jewish mythology/folklore and Lilitu is a figure from Mesopotamian folklore (who doesn't even have the properties that some pagans claim she does).
So, what am I, someone who was raised Christian and is now a diabolist eclectic pagan doing with Lilith as one of my patrons? Well, as you can see from the Sigil, I'm more invested in the Satanic perspective on Lilith -- though I do not deny her origins in Judaism (and trust me -- I've gotten in a lot of fights with facebook pagans about this and corrected a lot of false information being spread about Lilith.)
To me, she's a sort of figure of self-determination. That given the choice between subjugation in paradise or freedom in the desolation of the desert, she chose freedom. To be oneself and do what one believes is right for themselves, no matter what. And also, as a hedonist, there are definitely parts of her myth that are uh, deeply appealing.
In the end, Lilith doesn't really belong to me so I'm not going to go on at length about her meaning to me, about how I see her and etc., because there's already a lot of misinformation about her out there and I'd much rather let Jewish voices define her.