I think it depends on how you see your definition of "best".
If it means "most skilled", no Lebron isnt the best. If it means "most effective", then yes Lebron is the best.
Personally, I think "most effective" would be more fitting. Going back to Shaq... if you could have one possession where either Shaq or Timmy could go at a defender one on one in the post, who would you trust more to take that shot? I think most people would take Shaq, simply because he is too physically dominant for any one person to handle, even though Timmy is undoubtedly a more skilled post player. Or another comparison, would be Dirk and Nash. Back in the day, they would always have shooting compe ions, and Nash would generally beat Dirk. But who would you rather have take a big time jump shot? Most would probably say Dirk, because he is a more effective shooter than Nash (largely due to his size), even though Nash is a more polished shooter.
In each case, the general consensus would say that Shaq in his prime was a "better" post player than Duncan, and that Dirk in his prime was a "better" shooter than Nash.
If Lebron is the most unstoppable player in the post, I think he deserves the le of "best" post player, even though Timmy, Gasol, Carmelo, Kobe, and Bynum are all more skilled and polished post scorers.