Lex Luthor is all about the money and the cunning. Supposing he changed the world oil currency to African Gold Dinars from the US Dollar? That would piss a few people off, especially those that had no gold, and also countries who had to deplete there gold stocks to buy the oil in the first place. Add to that some ANON or LOLZ hackers and you don't need to touch nukes - pressing a button is too easy, there's hardly a story in it except for blackmail, like Kim Jong at the moment. He isn't even being taken seriously, not this side of the atlantic anway. Maybe a Julian LaSange type whistleblower character is his secret weapon? You could also make him the new CEO of facebook where he kept control of a voluntary world wide database and keep track of just about everything they do in life. I'd go with the electronic / banking systems corruption - much more Lex Luthor like. Oh wait... sorry you want fiction... all this is already going on...
World war 3 started the day after world war 2 ended; and we have been living in it ever since. It is the fight over the 3rd world. The only way it will end is if we form a world government, we somehow end-up in an uneasy but stable stalemate, or we all just get tired of killing one another.