Interesting thought, but from what I understand, the current consensus is Papa Raith gets his immunity to enemy magic from HWWB. Deirdre's Denarian was on Team Nic, and wouldn't cooperate with the Walker. Opposing agenda.
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From where we last saw her, Lara isn't in a great position. She could be persuaded to take more power.
Yes, the WN Deeps Battle devastated (not decimated) her opposition in the White Court, and let House Raith effectively take control. I imagine it will take the other houses decades or centuries to become contenders again. However, her House was wounded as well, and with Papa Raith (please make that a pizza joint) on a leash, the other houses were still somewhat beholden to her bidding. Their losses count as her losses in any conflict where the White Court would stand unified.
Also, remember Shagnasty. That Skinwalker waltzed right into Raith manor and made a field day out of ripping her personal guards apart in her very home. News of that demonstrates vulnerability, and news like that spreads. It also must have rattled her.
The Circle - who are all but confirmed to be Outsider affiliates - was trying to take Lord Raith out in White Night. It's possible that how the shield was set up means the Outsider(s) are stuck sponsoring it no matter who Raith is controlled by, so long as he lives. But I'm not sure the shield means he's necessarily still immune to everything Harry can throw at it anyway. Harry has learned a lot since BR, including getting better at recognizing Outsiders' handiwork, and that he has some sort of edge over them that other wizards don't.I'm thinking it might not be a coincidence that the death curse Margaret was able to tag him with despite his "invulnerability" was cast as she was giving birth to a starborn. Winter's power might be another advantage, given how hard it reacted to the other walker he fought in CD when combined with soulfire.
As for Lara' position, it's also relevant that Thomas mentioned in CD that the expansion in her power base has been getting scarily significant lately. I doubt she'd be hard pressed to keep Skavis and Malvora in line if she had to now; it's just that under white court culture she just prefers manipulation even after growing beyond absolutely needing it. Plus, there are probably other ambitious members of her own family that would decline to exactly fall into line.