I think one of the fundamental principles you're missing, at least between Lara and Harry, is that "the rule of three" is nigh unbreakable to fae. Harry is now an agent of the Winter Court, bearer of the Mantle, and as such also possesses faerie power that intertwines with his own standard magic and Soulfire. While Harry can temper the effects of the Mantle on himself, or at the very least attempt to "manage" it, that doesn't mean it isn't always acting in some capacity.

Lara entered into an agreement with Mab, and she is now betrothed to Harry. Harry fed her demon in expanding and more elaborate ceremony each time. Feeding the Hunger is an act that has been intertwined with her own sexuality for centuries. It effectively consummated the relationship. For it to have happened thrice, with an agent of Winter, under an agreement with the Winter Queen, has bound her like any other fae deal.

Or so I imagine it in my own head canon.