Watched The Double the other night and I have to say, at this point I have no doubts about Eisenberg's ability to pull off Luthor. No, he doesn't quite fit the physical appearance of the classic Lex, but he has more than proven his ability at this point to play extremely intelligent, charismatic figures. After all, when he was bald, Gene Hackman was a dead ringer for the comic book Lex, but his performance came off more as a '60s Batman villain (largely due to the screenplay) . And I feel that in the context of the current superhero movie boom, fidelity to the source material has become more highly valued.
At this point, I imagine Eisenberg's Luthor to be somewhere between his performance in The Social Network and the more outgoing and charming of his two characters in The Double.