Akkadian Mythology:  Lilith has been identified with ki-sikil-lil-la-ke₄, a female demon in the Sumerian prologue to the Gilgamesh epic.

Kramer translates:

a dragon had built its nest at the foot of the tree

the Zu-bird was raising its young in the crown,

and the demon Lilith had built her house in the middle.

[...]

Then the Zu-bird flew into the mountains with its young,

while Lilith, petrified with fear, tore down her house and fled into the wilderness

Wolkenstein translates the same passage:

a serpent who could not be charmed made its nest in the roots of the tree,

The Anzu bird set his young in the branches of the tree,

And the dark maid Lilith built her home in the trunk.

The Gilgamesh passage quoted above has in turn been applied by some to the Burney relief (Norman Colville collection), which dates to roughly 1950 BC and is a sculpture of a woman who has bird talons and is flanked by owls.  [This connection is one of fantasy rather than logic—jk.]

The key to this identification lies in the bird talons and the owls. While the relief may depict the demon Kisikil-lilla-ke of the Gilgamesh passage or another goddess, identification with Lilitu is more tenuous and likely influenced by the "screech owl" translation of the KJV. A very similar relief dating to roughly the same period is preserved in the Louvre

The Britannica writes of Lilith:

female demon of Jewish folklore; her name and personality are derived from the class of Mesopotamian demons called lilû (feminine: lilitu). In rabbinic literature Lilith is variously depicted as the mother of Adam's demonic offspring following his separation from Eve or as his first wife, who left him because of their incompatibility. Three angels tried in vain to force her return; the evil she threatened, especially against children, was said to be counteracted by the wearing of an amulet bearing the names of the angels. A cult associated with Lilith survived among some Jews as late as the 7th century AD.

Erubin 18b says that after the expulsion from Eden, Adam was separated from Eve for 130 years, during which time the seed he wasted created "ghouls, demons and lilin". I. e. in Talmudic tradition, not Lilith but Adam engendered the lilin, a connection that may be the origin of the later association of Lilith and Adam.

In some passages of the Kabbala, as well as in the 13th century Treatise on the Left Emanation [2], Lilith is the mate of Samael.

In others, probably informed by The Alphabet of Ben Sira, she is Adam's wife (Yalqut Reubeni, Zohar 1:34b, 3:19 [3])

The passage in Genesis 1:27 — "So God created man in his own image, in the image of God created he him; male and female created he them" (before describing a mate being made of Adam's rib and being called Eve in Genesis 2:22) is sometimes believed to be an indication that Adam had a wife before Eve.

A medieval reference to Lilith as the first wife of Adam is the anonymous The Alphabet of Ben-Sira, written sometime between the 8th and 11th centuries. Lilith is described as refusing to assume a subservient role to Adam during sexual intercourse and so deserting him ("She said, 'I will not lie below,' and he said, 'I will not lie beneath you, but only on top. For you are fit only to be in the bottom position, while I am to be the superior one.'"). Lilith promptly uttered the name of God, took to the air, and left the Garden, settling on the Red Sea coast. As a side note, this places Lilith in a unique position, for she left the Garden of her own accord and before the Fall of Man, and so is untouched by the Tree of Knowledge. However, according to legend, she also knows the "true name of God". The Alphabet of Ben-Sira is the earliest surviving source of the story, and the conception that Lilith was Adam's first wife became only widely known with the 17th century Lexicon Talmudicum of Johannes Buxtorf

The background and purpose of The Alphabet of Ben-Sira is unclear. It is a collection of stories about heroes of the Bible and Talmud, it may have been a collection of folk-tales, a refutation of Christian, Karaite, or other separatist movements; its content seems so offensive to contemporary Jews that it was even suggested that it could be an anti-Jewish satire [4], although, in any case, the text was accepted by the Jewish mystics of medieval Germany.

Lilith then went on to mate with Asmodai and various other demons she found beside the Red Sea, creating countless lilin. Adam urged God to bring Lilith back, so three angels were dispatched after her. When the angels, Senoy, Sansenoy, and Semangelof, made threats to kill one hundred of Lilith's demonic children for each day she stayed away, she countered that she would prey eternally upon the descendants of Adam and Eve, who could be saved only by invoking the names of the three angels. She did not return to Adam.