What if I skip this execution (like I am doing it now by exploring and completing other quests), discover true about Lord, and back to execution location?
I guess it will be too late in this case?
It's one of the few quests that's on a timer: once it starts, you have a set amount of time to intervene otherwise the execution goes ahead, rather frustratingly.
I'm not sure how to get past the persuasion check: my main character wasn't able to pass the first one (but did the second) and she already has quite high persuasion; I tested it out by respeccing and still failed the first test, though I didn't do so particularly exhaustively.
Not sure about Malady's intervention in Lohse's quest: I suspect that one may have some wrinkles that still need to be ironed out.
