I think that Oswald made up his mind at least by Thursday when he tells Frazier he wanted to get curtain rods, so he had a cover story for his brown paper rifle bag that he was planning to take to work on the Friday morning.
But the following exchange with Marina is interesting, was Oswald looking for a reason not to do the deed or was he hoping to get Marina's hopes up, then screw her over or perhaps deep down he knew that his marriage was over and just wanted confirmation?
This is why this sort of stuff continues haunt me. It all seems very unlikely for a committed assassin. It sounds very much to me like someone who was trying to find a reason not to follow through with the assassination. It could be viewed as his excuse for why he came to Ruth Paine's on a Thursday, but those seem like very specific conversations and promises if this was his purpose. What if Marina had said "Super, I'll ride in with you and we'll look for an apartment together."
A typical LN response is "He did it, damn it, it doesn't matter why or what he was thinking." I disagree - there are several weak spots in the LN narrative, and trying to piece together Oswald's motive and explain his attitude once he was in custody are, IMO, right at the top.