The legend is;
Inanna finds a huluppa [poplar? willow?] tree in the Euphrates river, it having been blown down in a storm. She plants it in her sacred garden in Uruk, hoping to see it grow big enough to make a throne and a bed from. 10 years pass, and a serpent that can not be charmed makes its nest in its roots, the Anzu-bird [a great eagle with a lion's face] builds a nest in its branches, and Lilith takes up residence in its trunk. Inanna weeps and in despair implores help from her divine brother Utu, the sun god, but he refuses to come to her aid. She then turns to her mortal brother Gilgamesh, King of Uruk, and he puts on his armour and takes his axe, and enters Inanna's sacred garden. Approaching the huluppa tree he strikes at the serpent in the roots, the Anzu-bird flies off with his young to the mountains, and Lilith smashes her home and flees to the wilderness. Having cleared the tree of these pests [or are they it's protectors?] Gilgamesh cuts down the tree and carves a throne and a bed from its trunk for his divine sister. From the roots of the tree Inanna fashions the emblems of kingship and gives them to Gilgamesh. These emblems Gilgamesh later abuses, and the earth opens and they fall into the underworld.
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The image of a tree with a serpent at its roots and an eagle with young in the branches, reminds me of the Norse world tree, Yggdrasil, with a dragon gnawing at its roots and an eagle in the uppermost branches with a hawk sat between the eagle's eyes. Perhaps Lilith (and Inanna?) parallel the Norns who water the tree as well as direct the fates of humankind.