The situation with Fox wouldn't really have any bearing on the OOT specifically. As far as I know, their ownership extends to any and all versions of ANH but everything else belongs to Lucasfilm.*

Between 3D and 4K, there are two more opportunities to squeeze more money just out of the SE. But like I've said before, those still aren't good enough reasons to get people to shell out for these movies in significant numbers yet again.

*I've heard some people incorrectly speculate that that's why Lucas created the SE in the first place, to get his own copyright on ANH.