I think Green has done pretty well on him. If you don't just look at the numbers and actually watch him play him every time he is making Lebron work for his points. Lebron is just making some difficult shots and one's that he usually struggles with. Of course he'll have the occasional blow by of Green but I think Lebron does that against everyone in the NBA.
I agree, I think Green has done well against him, when they have been able to keep the Heat out of the open court. The numbers look bad, mainly because when Green was in there, the Heat were getting a lot of fast breaks, and Lebron was attacking before the C's were able set the defense. IMO, it has had a lot to do with the offense when Green was in there (or more accurately, when Pierce was NOT in there) not being able to take care of the ball, and convert baskets.
When the defense has been able to set up, I think Green has done a very solid job on Lebron, by being aggressive, fighting past picks, etc.
...although I do wish he would get better in the team defense.