The Bible mentions the Lilith only once, as a dweller in waste places (Isaiah 34:14),
Wildcats shall meet with desert beasts, satyrs shall call to one another; There shall the lilith repose, and find for herself a place to rest.
So she obviously existed.
Lilitu were regarded as desert-dwelling demons. There wasn't a singular "lillith", but these were a class of malevolent spirits which were believed to exist in the desert wastes.
In
much later Jewish folklore the concept of the lilitu or lilith evolved based on certain legends and rabbinic traditions which arose in the Talmudic and post-Talmudic period.
Where in the biblical period lilitu were understood as malevolent desert spirits (and are mentioned by other non-Jewish sources of the Near East as well), by the Middle Ages "Lilith" evolved as a way by certain rabbinical teachers to reconcile the discrepencies in the Bible.
Specifically here is the discrepency between the two creation stories in Genesis 1 and Genesis 2. In Genesis 1 it reads that God created human beings (adam) both male and female. In Genesis 2 it reads that God created the first male human (Adam) and then later created the first woman (Eve) from Adam's rib. So rabbinic teachers asked a natural question: Were Adam and Eve created simultaneously (as in Genesis 1) or created separately (as in Genesis 2). Some rabbinic commentators suggested that Adam had a first wife, the female of Genesis 1, but something must have happened because she is no longer around by the time God created Eve from Adam's rib in Genesis 2.
So the story arose that Adam's first wife was Lilith, but that she was arrogant, and so God cursed her and she was expelled from Paradise to dwell in the desert wastes as a hungry malevolent spirit. Adam, now wifeless, needed a wife, and so God created Eve from Adam's rib. Where the first wife was arrogant because she declared that she was created at the same time as Adam, God made sure that by creating Eve from Adam's rib that she would know her proper place as the wife toward her husband. Thus this also provided a lesson used by rabbis to enforce wifely subservience to their husbands.
None of this that I've described is actually biblical. It is legend and folklore that evolved from an attempt to address what some rabbis saw as a discrepency between the two creation stories in Genesis.
As for the lilitu mentioned in Isaiah, they were--as I said already--regarded as malevolent spirits that inhabited the desert and wastelands. Were there actually malevolent spirits that inhabited the desert? This is likely the Prophet Isaiah relying on a popular belief rather than a confirmation of the actual existence of malevolent desert spirits; these were entities of ancient near eastern mythology, and Isaiah's use of it to describe desolation as part of the larger motifs of the passage shouldn't be taken to meant as a direct confirmation of the existence of such things.
Alternatively, some speculate that lilit might correspond to some nocturnal creature, the KJV translates this as "screech owl" taking a more naturalistic interpretation.
Ultimately, the point isn't "these things actually exist", so much as "this is what the coming judgment looks like", reducing the judged nations as desolate as the harsh desert wastes.
-CryptoLutheran