Firstly, let me say, I do not think it will happen, primarily because LBJ is SUCH a great scorer, that it is in his teams' best interest for him to be the first scorign option. But that said, I do believe he COULD average a triple-double if he was that much of a stat whore.
He would have to play the role of a past-first PG on offense (the thing is, though Miami is a very talented offensive team, LBJ is still the best offensive option, so it just doesn't make sense for your best option to be always looking for others to score first). If LBJ did this, I've no doubt that while his scoring average would dip to the high teens, he would be able to average double-digits in assists.
On the defensive end, he would have to play PF. This he does a lot already and on nights when he does, he often comes away with double-digit in rebounds.
Now again, I say, this WILL NOT happen, but I honestly believe that if LBJ's goal was to do it, he would be able to. All he would need is the coach to let him play PG on offense, and PF on defense.
Do you think LBJ could average a triple-double?