@dezaki I think the caveat is that the Church isn't imprisoning him, he is free to leave whenever he wants, and it's his choice to stay. Then proceeds to use the persuasion ability to "suggest" to Liliam that the world is impure and dirty, he shouldn't leave, and he is much safer inside with them. So unless Liliam himself explicitly states he wishes to go out, he is "free" to leave whenever he wants. This is probably where the [Obedience Contract Canceller] will come into play and help him think for himself, but he will have to sort through years of conditioning and suggestions if he really wants to go out.
I do think she could have lied and said, "Gaia ordered me to visit Liliam" in order to get to him. They could still claim he's sick, but then she can counter that she is also a legendary healer that can heal him. Not sure what other arguments they can use to keep him from her, since she would be using their God as the reason she needs to visit him. Also considering I'm not sure any of them actually talk to Gaia like the Demon Lord can, more of a worshiping a deity they know exists but can't communicate with, I don't think they can claim Gaia told them differently. But, knowing how shady they are, they'd probably use that card regardless.