About Lilith and Lilim: As it turns out, the "Adam's first wife" myth is one of quite a few myths about Lilith. In that myth, Lilith fled from Adam (The reasons are still discussed, but it's about sex or physical attraction, that much seems certain), met the king of Demons, Asmodai, and bore thousands of demons. Those demons are known as Lilim (Male plural)\Lilin (female Plural) or Lili (singular). Her children are commonly reffered to as Lilim because in Hebrew, when speaking of a group, as long as there is a single male, the whole group will be reffered to as male. Lilith's children, the Lilim, are said to constantly hunt Adam's children.
About the Sephirotic Tree of Life: First off, this isn't a tree of life-The Tree of Sephiroth hints towards ways to divinity, of becoming closer to God. (This could be something false, though, so I can't really gurantee this). Another thing that is noteable should be looked upon in this picture, where you see Rei standing in the Malkhuth sphere. Upon research, the results given were:
Hebrew Wikipedia wrote:Malkhuth, also known as 'Residual', is attributed to feminity, and it takes from the Yesod sphere what is given by God and trasfers it into the Physical world. It is not active, but passive, and alone it has nothing, a mere container. This fits the feminine description it gets.
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Of the other side of Divinity, Satan, it is said that he is intresed in 'conquering the Malkhuth', to take over the Divine abundance that will reach the residiual Sphere.'
This is a literal translation, but I think it's fairly intresting to compare it to Rei, who is a figure that is attributed to maternal and feminine features throughout the series.