I don't really wanna bypass the other problem with what @chaosevilspacewitch said, which is "Judeochristian." Lilith is not a part of Christianity, and never has been.
Like it's really really important to recognize that!
She was not subsumed into/incorporated into Christianity at all, and so she cannot be a subversion of "Judeochristian patriarchal mythology."
Judeochristian is a highly problematic term for a VARIETY of reasons, and people shouldn't use it (outside of, perhaps, the first three centuries CE, where Christianity was still defining itself as a unique religion) because they will inevitably say/imply some shit that just isn't true! Like suggesting that Lilith is a part of Christian mythology in any way. She isn't.
Like @penrosesun mentioned, the idea that she was Adam's first wife is from a deeply misogynistic text. She's not really a girl boss there. She actually leaves and is told if she doesn't return 100 of her demon children will die every day. And she agrees to that and declares she was basically made to bring pain and death and likes this. So. Not exactly a good thing.
Things associated with Lilith in various jewish texts:
Tragic death of infants / committing infanticide (particularly of disabled, unhealthy, or "strange" children)
Birthing demon babies that will die in the hundreds (possibly even killing her own children)
Miscarriage (especially with genetic defects)
Giving children epileptic fits
Causing death in childbirth
Having hundreds of agents of like...evil and badness
Being the partner/consort of a demon prince/king (Samael/asmodeus)
Nocturnal seminal emissions
Possibly the first mention of Lilit is just referring to a screech owl/night bird. She does show up in the talmud (predating the alphabet of Ben Sira, aforementioned misogyny text) but all of those earlier mentions seem to be limited to her being a horrifying demon.
Rabbi Ḥanina said: It is prohibited to sleep alone in a house, and anyone who sleeps alone in a house will be seized by the evil spirit Lilith
Niddah 24b discusses miscarried fetuses that resemble the form of "a Lilith", who appears as a woman who has wings. But this suggests it's a category of creature, not a singular woman.
[[ I've seen one really good tackling of a more feminist (less misogynistic than Ben Sira) reading of Lilith that I greatly enjoyed but CRUCIALLY, it didn't erase her connection to infant mortality or to Judaism. It's the middle grade graphic novel, The Unfinished Corner.]]