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Alastor Theory
Okay, I'm gonna throw my hat into the ring when it come to who has Alastor on a leash and I'm not gonna say Lilith.
I think Eve might also be an option for being the one that owns Alastor's soul.

I think the Lilith connection is a bit too obvious and Lilith hates being forced into subservience canonically within the show, so it would be weird if she chained another soul to do her bidding. And Eve is easily the character that would have the most issues with the Morningstar family, heaven, and hell. She was made out of Adam's rib and given the apple by Lilith and Lucifer. She's been a pawn in other people's plans since the beginning. She's the one blamed for original sin and it's clear she's not in heaven. She was the scapegoat while Adam got off relatively Scott free.
She has so many reasons to want to get back at everyone and what better way to gradually gain a foothold without drawing attention to herself than enlisting the services of a sinner in hell?
It’s said that Alastor immediately started taking out overlords that had been dominant for centuries the moment he stepped foot in hell. There has to be a reason for that. It feels too calculated to be a coincidence.
Plus Lilith’s disappearance coinciding with the Alastor's isn’t necessarily a factor against this theory because it can be explained as Eve essentially throwing Alastor into a battle with Lilith where Alastor was injured and had to take time to recover.

His reaction when Zestial said people thought he had been struck down by holy arms was a bit telling to me. The way he took that moment to look away and collect himself to brush it off read as Zestial hitting too close to the mark.
He's super touchy about why he was gone for 7 years and we've seen that Alastor's berserk button is his pride and he dislikes his strength being questioned. He absolutely would not want to admit he was gone because he was recovering.
That comment seemed too pointed by the writers to be completely written off.
Maybe in this battle Eve got Lilith's soul. If she doesn’t why would Lilith be gone from Charlie’s life for seven years? Why wouldn't she return around the same time as Alastor? She seemed to really care about Charlie. Charlie still tries to call her and she doesn’t seem to hold any resentment toward Lilith, so I think there would have to be a reason beyond nebulous plans that's keeping her away.

Alastor also clearly does not have a good relationship to whoever has his soul, so I kind of imagine if it was Lilith he would be a bit more hostile towards Charlie or it would show a bit more in the moments where he was alone or when Charlie isn't looking. (Alastor is the only character this show is truly subtle with)
I just wanted to put my opinion out there because I've seen so many Lilith owns Alastor's soul theories out there and I wanted to offer a different angle.