I really don't understand why there is a young Lex Luthor yet Batman is supposed to be older (late 30s, 40s?). That really shits on the lore.
No. Superman and Batman will be meeting for the first time and Lex Luthor is a Superman enemy, so his age in contrast to Bruce's is irrelevant. It'll probably be the rise of Lex Luthor, and Batman will likely be an established hero whereas Superman is new. Superman is already ~30 in Man of Steel, so Batman will likely be in his very late 30s or somewhere in his 40s. They don't have any frequently-established constant age difference, so saying it "really shits on the lore" is pretty wrong. Anyway, Jesse Eisenberg (who's playing Lex Luthor) is the same age as Henry Cavill (Superman), so that's all that really matters (though it wouldn't really matter if he wasn't, because changes are fine as long as they work out).
This is one of the reasons I dislike superhero comics and their movie adaptions. Why don't they follow any sort of canon? It's like each issue is in it's own universe. It's fucking retarted. I guess it actually takes skilled writers to follow a loose timeline and not write a bunch of crap with plot holes and continuity errors. Is that why they're always retconning things in comics? Also, how is Lex's age irrelevant because he's a Superman villain? They live in the same universe.....
Like I said earlier though, the movie adaption is just that. The director will do whatever the hell he wants with the source material, even if it shits on the lore (which it does even if you deny it). Snyder has stated that this movie will show Clark and Lex as friends (and probably when they become enemies as well), which is supported by the comics, but they were not 30 years old when that happened, they were younger... teens & 20s. Lore. Shit on. But of course, due to the nature of comics, anything is possible. Doesn't mean I have to agree with it. A good story doesn't need to be changed every iteration.
I could see Eisenberg playing a young Lex Luthor with hair in flashbacks. I would like to see that.