I've also heard about some football quarterbacks who do this, notably the Manning brothers and Tom Brady. They keep extensive notes of what happens both in practice and in competition, and it shows. They have five super bowl championships between them.
I recently also read about how Michael Vick claims to have been "the last to arrive and the first to leave" practices and team meetings when he played for the Falcons. Michael Vick has not won or even appeared in a Super Bowl.
There are obviously many things that go into a championship in any sports. And one of them is certainly the realization that talent alone will not win a championship at the highest level. There will eventually be other players in the field or match or game that are equally as talented and are also trying harder.
There is a certain "championship" mentality. I think Kobe Bryant has it. He berates team mates to get better, expects improvement, expects clutch performance. At times he demands it. This mentality drives some people away, notably Shaq, but also many lesser players like Smush Parker, Kareem Rush, Gary Payton, etc.
Kevin Garnett is also a standard setter and enforcer. He loves to practice, loves to set the bar high and then see if anyone can exceed it. Garnett is a champion.
To improve, to succeed, to win, one must really embrace all facets of competition: practicing, mental preparation, and competition. Lacking any one these things represents a flaw that will eventually be exploited.
We often don't know the true persona of a team until it has passed; until the heat has been turned up high and we see what they are made of. If they succeed then we look back for tiny clues of their future success. If they fail then suddenly there appears a million hints, a million reasons.
Does LeBron has this? I don't know. What has he done to expand his game?