A source, who is very close to Lebron has reportedly said that Lebron will not be playing for the USA International Team in 2013 or 2016. He could be doing this for a couple reasons.
Number one, Lebron might have decided that he's proven enough to the world. He might have decided that everyone knows I'm the best player in the world, and it doesn't matter now. Number two, he wants to have a relaxing off-season. Maybe Lebron wants to spend more time by himself, or with family. Number three, and in my opinion the least likely, he's having trouble with teammates or people part of the USA Team.
Either way, Lebron will not be playing for the USA Team in 2013 World Championships or the 2016 Olympics. I still believe USA will gold in the World Championship (Lebron wasn't even on the team then, and they still won gold). However, the Olympics is tough. Kobe might be out of the league in 2016, and if Lebron doesn't play, that leaves Kevin Durant to be the best player.
Can he do it? Well it depends on who's joining the team. Lebron is very influential, and if he doesn't play, others might drop out too. If other players leave, it's hard to decide. However, if the roster in 2016 is the same as one in 2012 (with two added players) I still believe they will win gold. They still Melo, Durant, Chris Paul, (hopefully Dwight Howard), Russell Westbrook, etc. Besides, Durant won the 2012 Gold Final against Spain in 2012. He had 30 points, 9 rebounds, and shot 8-18 from the floor!
He has proven he can lead his team to victory, and I believe he will do it again in 2016.