I don't think we could see a losing team's player win the MVP. Like I literally don't think it would be allowed by the league. Nor should it be, imo.
I don't think Lebron has earned that yet, either. He has great totals, but also some of his stats/numbers aren't that great. Low efficiency/percentages, mainly. There are plenty of players that could put up gaudy numbers if allowed to hero ball in the finals, and if he's the best player in the world as he claims then good numbers is the minimum expectation. He does it better than most, but the gut check also can't ignore the fact he's also disappeared in a few 4th quarters or overtime and taken plenty of plays and quarters off, becoming the aloof jump shooter he can sometimes be, showing the side of him that used to be pretty frequent where he pouts and let the team fail just so he could smugly let everyone realize how great and needed he is.
That's always been how he operates, though, and part of it is that I honestly don't think he cares that much about winning. If he did, instead of pointing at his stats and saying he's the best player in the world so he isn't worried, he'd be out there not disappearing even if he's tired, or he'd at least be focused on how to win, not how to advertise himself. So, yeah, he claims winning is number one, because that's every athletes stated goal, but it always feels like a side effect with Lebron. His goal is all that bullshit he talks about all the time about being a mogul and brand. Other players have done it purely through winning. But honestly, Lebron has never had to even win to accomplish his goals, and I think it hurts his underlying motivation.
Sure, if he wins it helps cement his legacy, but in his mind that's already cemented. He's in a position I've often felt he actually favored (or at least seen how he can benefit), where there isn't any pressure to win, and he doesn't really have to care all that much about winning. He has to say he does, but can then disappear on the court for stretches or entire games so everyone can remember how important he is. In the end, though, he's in a fine position that helps his overall brand by being selectively amazing and when he wins against all perceived odds he gets all credit, and when he doesn't win a game or series his supporters can blame a lot of other factors the way it has always been in Cleveland.