I didn't read the fan theory, but I also got the impression that the events are sperate timelines. But, there's a couple problems with that. Mainly, the head Security guy Ashley (he's a Hemsworth), who has done nothing but talk about how the hosts can't be fully trusted, it's only one line of code that stops them from killing people, stuff like that. Highly unlikely he is a host.
And then there's the Delores story. She's obviously changing before and while on this quest with William. But, is that happening at the same time as her meetings with Bernard, and now Ford? It seems unlikely that she could have changed that much in the past, and then again in the current. Plus, there's the Ashley connection, where he referenced MiB and Delores while she was with William.
As for Lawrence, the last we see him with MiB, he's left hanging upside down and the kid is told that someone will be along shortly for him. Maybe he was cleaned up, and put back out at the starting point of his narrative. Maybe MiB saved him from the noose at a point further along in Lawrence's narrative.