Actually Lilith does appear in the Bible under the archaic name Iamia, in Isaac 34:14,
No name, look in Isaiah 34:14 NIV (none also in KJV translation)
Desert creatures will meet with hyenas, and wild goats will bleat to each other; there the night creatures will also lie down and find for themselves places of rest.
I've looked up the meaning of "Lamia" which is a name of a queen of Libya who became a child-eating demon. Indeed, Lilith is also a child-eating/killing demon. But that is not mentioned in Isaiah 34:14.
Lilith in Jewish Literature also flew to the desert with a pair of huge wings to find rest from her tormentor - Adam, the first man.
Just like the anointed Woman of Revelations whom many say is the mother of Jesus or Israel, also were given wings (by God) and flew to the desert to escape her tormentor, the dragon.
One Egyptian Goddess with one of its many titles as "Queen of Heaven" is also mentioned as Queen of the desert and jackals. She also had a crown of stars just like the Anointed Woman of Revelations.
While the Anointed Woman of Revelations in addition, was said to have the moon under her feet.... The moon is virtually a barren, lifeless world, like a desert...
Lilith also shares similarity to Isis for knowing secrets unknown to anyone else but God only. Isis was capable of all the miracles performed by Jesus
I honestly don't trust the fewer negative depictions of Lilith as she parallels more positive characters elsewhere.
Perhaps, it just happened that Lilith was probably a woman with spectacular abilities (like the consistent description of her ability to fly) and under a misogynistic patriarchal society of The Jews who could not accept a woman having great powers over a man, they decided to turn her into a demon in their stories.
I mean who really murders children even from the wombs of pregnant mothers?? It's not Lilith.....before abortion, invading armies of men usually did such atrocities and they're still doing it today.
Logically - speaking, the Lilith myth would have made an excellent false propaganda to find someone else to blame for the atrocities of men and to perpetuate a patriarchal society which was endemic all over the world prior to the 21st century.