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Yes. Lacie is the mother of Alice and her twin sister The Intention/Will of the Abyss, Revis reaffirmed this when he said he impregnated Lacie and forced her to give birth in the Abyss. "Alice and the Intention are twins who were conceived in the human world and born in the Abyss." Alice returned to the surface world and the Intention stayed because the Core chose her as it's vessel.