| Quote #1
He had turned into a dragon while he was asleep. Sleeping on a dragon's hoard with greedy, dragonish thoughts in his heart, he had become a dragon himself. (6.32)
Transformations in Narnia usually consist of the outside of something suddenly looking like the inside. Because Eustace behaves like a cold-blooded monster, he becomes a terrifying reptile. Consequently, we can guess that, in order to turn back into a boy, he'll have to start acting more human.
| Quote #2
In spite of the pain, his first feeling was one of relief. There was nothing to be afraid of any more. He was a terror himself now and nothing in the world but a knight (and not all of those) would dare to attack him. He could get even with Caspian and Edmund now....
But the moment he thought this he realised that he didn't want to. He wanted to be friends. He wanted to get back among humans and talk and laugh and share things. He realised that he was a monster cut off from the whole human race. An appalling loneliness came over him. He began to see the others had not really been fiends at all. He began to wonder if he himself had always been such a nice person as he had always supposed. (6.34-35)
Becoming a dragon gives Eustace the ability to see himself for who he really is: an unpleasant, selfish person who is a burden and blight to everyone around him. Once he recognizes this, he is better able to understand his companions and their motivations.
| Quote #3
It was, however, clear to everyone that Eustace's character had been rather improved by becoming a dragon. He was anxious to help. (7.14)
Making Eustace's appearance match his behavior encourages him to change that behavior right away.