I think there's some similarities between Lecavalier and Dubois and maybe Tortorella feels the same and is trying to get the best out of him. The difference seems to be that Dubois doesn't see it the same way and is reacting differently than Lecavalier did
Im not sure Dubois is acting any different than Vinny did. Vinny didn't want to play for Torts and was very resistant to the change when Tortorella stepped into the picture. At the time of his trade request 20 years ago, he was getting skewered by some, just like Dubois is now. He's lazy, he's inconsistent, he doesn't play hard or show enough effort, he doesn't care about winning, he's just a young kid interested in his money, etc. Obviously that's not the perception we as fans hold of him today. Quite the opposite, as his #4 hangs from the rafters of Amalie Arena as a player & person that is celebrated and remembered as a great representative of the franchise.
Back then though Vinny was a training camp hold out, Torts sat him out games because of his conditioning, benched him, called him out publicly, and stripped him of his captaincy which he had been given by a previous head coach. We had veterans trying to guide him in the right direction off the ice as he struggled and didn't play well on it. It was very much publicized that the 2 had a rocky relationship and were not on the same page. That trade was very very close to happening. Obviously things changed and we remember all the good times that came later, but that doesn't mean that there weren't bad ones. In this case, potentially disastrous ones.