I would think it depends on the property. With something like Star Wars or Indiana Jones, it’s obviously LFL, so now owned by Disney. Trickier to know where the rights lie with co-productions I think.
So something like The Land Before Time, if the other movies are anything to go by, I think Universal must own that. Something like Willow, where it’s LFL and Ron Howard, I’d imagine (heh) that that’d probably end up being something Disney might want them to look into.
Personally I’m most curious about Labyrinth. With the Jim Henson Company doing new Dark Crystal stuff, I wonder if they’d be interested in continuing the Labyrinth universe in some capacity, and if so if LFL would be involved.
But honestly, if I had to guess, Disney probably only cares about Star Wars and Indy from them in terms of IP, and otherwise the company will probably focused on coming up with new IP potential. Especially if the talk is true that Fox will soon cease to produce much more than preexisting IP movies, and if Disney continues to produce solely live action remakes and sequels (and the occasional kiddie flick), it makes sense to have a banner like LFL be making new, more-adult-skewing (though still family friendly) content. If someone doesn’t come up with new stuff eventually, they’re going to be in trouble.