That's just arrogant, imo. Why not study LeBron's game? Unless he's just playing mind games (thinking about it, this is pretty likely).
Kobe doesn't study Lebron.... Why would he? Lebron's game is on most part a product of his size and athleticism. Kobe's game on the other hand is a product of things like foot-work, focus, skill, and overall knowledge of the game. Lebron stands to learn much more from Kobe than vice-versa. I also think that individual battles as far as numbers go over a season or from night to night is beyond Kobe at this point in his carreer. He has realized that no matter how many points he scores or how many stats he racks up from game to game, the only thing at the end of the season that matters is a championship. I think Lebron knows this aswell but that he is still trying to overtake Kobe. Therefore Lebron would be more interested in what Kobe is doing every night.
I would be thinking he's scouting our potential opponents for the next round. We're not even guaranteed to have to face LeBron, so why waste time with that right now?