For a player on a losing team to win the MVP, I think the following needs to happen:
(1) Nobody on the winning team can have a dominating series = so far so good for LeBron. Steph and Klay have been up and down. Iggy has been their best player from start to finish. Iggy has played very well but he hasn't been special. If Steph Curry has another massive game in game 6 to lead the Warriors to the title, that could swing things back his way. Dominant performances in deciding games will make up for his weak showing to begin the series.
(2) the losing player's best guy has to be extraordinary. Not just excellent but phenomenal. The type of performance that will be talked about for years to come. Which LeBron has most definitely been = extraordinary.
(3) The series has to be close. Cleveland did this early on but lost the last game by a big margin. If they lose in Game 6 by a big deficit again. I think that costs LeBron the title. If LeBron pushes this to a 7th game, I think he can win the MVP. If LeBron loses in a closely fought game 6 where he is superb, I think he can win MVP.