He's 31 so he can't really run for President.
Yeah, that plotline would have to wait a few years to be viable.
Really, it only wouldn't be viable in BvS. Any Superman sequel could easily, and most likely will, be set several years later. So, theoretically, the very next Lex centric (from the villain side of the story) movie could feature a Les for Pres plot or sub-plot, or at the very least introduce it or its seeds.
Actually, setting it up for a full on President Luthor in a 3rd Superman film would be pretty sweet I think. A nice "trilogy" arc, building to the finally showing just why Lex truly is Superman's ultimate foe. Either that, or maybe make an actual 'DC Trilogy' film where Superman must confide in only Bruce and Diana, and keep it off the books from the rest of the League.
I mean, they ARE trying to take down the president.
It would be a useful way to write the League out of it. After a BvS and 2 JLA films, it can be hard to justify why you're "only" having 3 of them as the focus.
Considering this is done all the time in the books, for team ups, and solo adventures, it always seemed an odd concern to have for the films; why wouldn't Tony call on Steve in Iron Man 3 kind of thinking. It's not a hard thing to justify story wise, I think, but I guess you've gotta convince the studio big wigs of that.
Any who, enough tangents.