Several different explanations are offered for the custom of shalom zachar:
1) It is a thanksgiving meal. We are offering thanks to G-d that the baby was born safe and sound. Birth (especially in the past) was a very dangerous time for the(mother and) baby, so we thank G-d that the baby survived this ordeal.1
2) We come to console the child who has just forgotten all the Torah he studied while in his mother's womb (see Niddah 30b). For this reason many people serve beans or chickpeas at the Sholom Zochor, since these are foods served at the house of a mourner.
3) According to Kabbalah, a child is not ready to be circumcised until he has gone through a Shabbat, for the Shabbat provides the infant with the spiritual power necessary to enter into a lasting covenant with Hashem. (This is (one of) the inner reasons why the Brit is on the eight day, to ensure that a Shabbat passes). For this reason we make a special celebration on the Shabbat after the baby is born.2 [The advantage of this reason is that we can also understand why shalom zachars are only done for boys.]
Reason 1 would pertain to Lilith as Lilith is commonly understood through fallen natural consciousness as a "baby-killer".
Reason 2 would pertain to Lilith as Lilith is commonly understood to be a male's "first true wife" which fled Gan Eden and fallen natural consciousness; the male child is mourning her loss.
Reason 3 would pertain to Lilith as Lilith is understood through shabbat consciousness and the promise of finding and reuniting with her again.
Lilith, Lilith, Lilith, light of the Night divine (niddah 30b, Sefer Yetzirah 4:6, Niddah 16b [3,4,5]) ... all shalom zochor is filled with thoughts of Lilith.
1. Terumat Hadeshen, vol. 1, s. 269.
2. Based on the Zohar, beginning of Parshas Tazria.
 Sefer Yetzirah 4:6 - "The Talmud (niddah 16b) teaches that there is an angel called Laylah that oversees birth."
 Dr. Ellen Frankel on an ancient midrash on Laylah:
“When a baby is conceived, Laylah, the Angel of Night, brings the fertilized egg before God who decides its fate: whether it will be a boy or a girl, rich or poor, strongor weak, beautiful or ugly, fat or thin, wise or foolish. Only one decision does God leave in the hands of the unborn soul: whether it will be righteous or wicked. Between morning and night on that same day, another angel reveals to the unborn soul its future life: where it will live and where it will die and where it will be buried. And then at the end of nine months, the angel announces to the soul that it is time to be born, but the soul protests. The angel silences it: 'So God has decreed. Against your will you were formed, and against your will you will be born. And against your will you will one day die. Such is your fate.' Just before the baby is born, the angel taps it right under its nose, leaving a small cleft there. Then the angel extinguishes the light shining above the baby's head and it forgets everything it has learned during the previous nine months. And then the baby emerges into the world, crying and afraid. Each soul spends the rest of its time on earth recovering what it once knew.” (Ellen Frankel, The Classic Tales, 17-18). "You shall not fear from the pachad Laylah ..." Tehilim 91:5; Sha'are Orah, R' Yosef Gikatilla (fifth sphere, sixth gate)
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