A neighbor asked me about there being a woman created before Chavah. The only Jewish source I could find was a paragraph in the Medrash of Ben Sirah about the creation of Lilit. Are there any other sources that discuss her?
There are several meforshim that mention her.
As you pointed out in your question, the Midrash of Ben Sira brought in the Otzar Midrashim is actually quite important as it frames what Lilis would go on to become. It centres around Adam and Lilis' dispute over who was to be the dominant figure in the act of intimacy, namely who would be the one to lie on top. Upon not 'winning' the debate, she mentioned the sheim Hashem and flew away into the air. Her personality/character can be perhaps best summarised in three main ways:
1) The source of licentiousness, immorality and seminal emission etc.
It is this initial analysis of her being the one who wanted to dictate the act of ביאה, that has placed her as the source for שכבה זרה - seminal emission. The Gemoro in Shabbos 151b writes:
אָמַר רַבִּי חֲנִינָא: אָסוּר לִישַׁן בַּבַּיִת יְחִידִי, וְכׇל הַיָּשֵׁן בַּבַּיִת יְחִידִי — אֹחַזְתּוֹ לִילִית
Rabbi Ḥanina said: It is prohibited to sleep alone in a house, and anyone who sleeps alone in a house will be seized by the evil spirit Lilith. (Sefaria translation and annotation)
Also refer to the Ohr HaChaim on Bereishis 49:11
2) The Harmer of Infants
The end of the Midrash cited above talks about her as causing the death of infants. This theme is continued in multiple places:
- Bamidbar Rabbah 16:25 - "When she does not find anything else, she turns on children."
- Shlah, Torah Shebichsav, Vayishlach, Ner Mitzvah 17
- Zohar 1:14b
3) The Mother of Demons
- See Rabbeinu Bachya, Bereshis 4:22
- Rav Hillel Rivlin (a talmid of the Vilna Gaon) writes in his Kol HaTor 3:23 that she is seen as Samael's (the Satan's) wife. Also refer to the Ohr HaChaim quoted above.
- See Rashi to Niddah 24b - A foetus born in the image of Lilis - "A demoness that has the face of a human and wings"
- Yeshaya 34:14 she dwells amongst goat-demons