I watched Rodman a lot when he was a Spur, and he was total garbage at that point because his mind wasn't in it. In fact, his mind was only in it when he was playing for Daly or Jackson, the only two coaches who actually spent time understanding him and accepting him. When he was with the Bulls, he played a huge amount of low post defense because that's what the Bulls needed, Pippen and Jordan were more than enough to cover the perimeter defense, and to be fair, there wasn't anyone like Lebron playing back in the day with that combination of speed and power.
Rodman may lack in speed (slightly), but Pippen lacks in the bulk to stop Lebron in the post. If Miami is smart, an attack with Bosh in the high post, Wade slashing, Lebron in the low post, and Allen spotting up on the perimeter would be a fairly tough offense to stop, and is a good counter to the Bulls strength, which is perimeter defense. Create an offense from inside out (using Lebron, very much like how the Lakers used Magic in the late 80s), in order to draw the Bulls perimeter defenders in. In the post, speed will not be as important, and a guy like Rodman would be able to contain Lebron without using extensive double teams.
If Lebron plays on the perimeter, I still believe Rodman has some of the quickness and defensive basics to handle Lebron, him not demonstrating that side of his defense on the Bulls was more due to need than him not having it (I think).