I wouldn't go so far as to call him a quitter but when given major uphill battles to fight, he does turtle up some and decide not to fight the good fight to over come the odds.
He did it last night. He did it against Dallas in 2011. He did it in 2010 against the Celtics.
He's a fabulous front running competitor, maybe one of the best. But when it comes to comebacks and overcoming difficult odds to prevail, he has a history of just not trying as hard, not playing as hard and not seeming to care, as if the loss is inevitable.
I also seriously question his leadership skills. It tends to be more along the lines of "Watch me and do what I do" or "Give me the ball and I will lead you there." and then he tends to go all iso and take all the shots and be the guy with a usage rate somewhere around 40% or higher. Rather than getting everyone involved his leadership is let me do everything instead of properly utilizing the players around them to make the team as a whole better. His leadership abilities tend to be all about the individual, him.
Lebron has never come close to a usage rate around 40%. His playoff career average is 31.4 (regular season is 31.6). In Miami his high is 33.4 (the first title season). The second title season he was below 30 at 29.2 and this year was at 31.6. The three highest USG% in the playoffs for Lebron were all in Cleveland when his teammates were obviously much worse on the whole.
As for this series though, Lebron had something like 48 assist worthy passes, only something like 20 were actually converted into assists. One of the lowest rates you will ever see from someone with nearly 10 assist worthy passes a game. His teammates totally and utterly failed him.
The bottom-line is, you can't expect someone to bring the ball up the floor, generate the entire offense, guard the opposing teams best wing (or PF), play 40+ minutes a night, 100 games a year, and then provide him no real support when he needs it most.