Biblical: Lilith is Adam's first wife. She was created from sand like Adam, whereas Eve was created from Adam's rib. Lilith constantly pushed for equality with Adam (which in the old school Arabian/Hebrew culture was an absolute no-no) and refused to do what he told her. As I understand it she also had far too many children at too quick a pace. For her disobedience and other things she was booted out of the garden of Eden, at which point she swore to spawn children that would bedevil Adam's descendents for the rest of time. Eve was later created from Adam's rib in a bid to make a woman that would do what her husband asked of her.
Evangelion: Lilith is the 1st angel to be found by Seele, but the official 2nd angel because of her succeeding Adam in creation. She is crucified on a giant red cross deep within Central Dogma, a subterainian cave. She bleeds "LCL," which substitutes for oxygen when inhaled by humans. From her abdomen, dozens of pairs of legs sprout. She has the Lance of Longinus (the lance used to stab Jesus in the side to assure he was dead) pinned into her chest, and as long as it remains there, she cannot grow her own legs. On her face, is a purple mask which has the symbol of Seele [a triangle with 7 eyes, representing both the trinity (the Father, Son, and Holy Ghost) and the 7 eyes of God which are said to watch the whole world]. In the End of Evangelion, when Rei becomes one with Lilith, the mask comes off and she comes from the cross.