Lion king- I don't believe you can bring any food in that can't be sealed. Same with drinks, you can't bring any drinks in that can't be sealed. So no alcoholic drinks or soda with no tops. Water bottles and such are fine
Same thing goes for Nemo I do believe. We didn't care for the show so we only saw it once, but I do believe same policy.
Beauty and the beast and Lights motors action- you can bring food and beverages into the shows whether your able to seal them closed or not
You can most definitely take food and drink into Flights of Wonder. Beer and a pretzel and a great show - it's a can't miss on every single one of our trips.
Closed, indoor, air-conditioned (or heated) theater - no open food. If your drink bottle is sealed, they will let you keep it, but they will make you toss a cup with a lid/straw.
Outdoor theaters - I think uniformly at Disney - allow food and drink.