The lawyer is a dynamic character who initially agrees to a bet because of his own prideful determination to prove a point to the banker and others at their dinner party. When the attendees begin debating capital punishment, the lawyer comments that "it's better to live somehow than not to live at all." When the banker asserts that the lawyer could not even live for five years in solitary confinement, the lawyer raises the length of his voluntary confinement to fifteen years, and for no additional money. This demonstrates that he is equally as reckless as the banker.
Yet through his voluntary confinement, the lawyer changes. He reads a great number of books spanning a wide range of subjects. He plays piano and learns various languages. At the end of his confinement, he finds that the values of society are ultimately meaningless, and he intentionally gives up the millions because he no longer wishes to be a part of the world which he has grown to hate while in confinement.
Your thesis based on this internal conflict might look like something like this:
The lawyer is a dynamic character who ultimately finds society's values meaningless, who believes that humans ignore things of eternal significance, and who willingly forfeits millions of dollars because he prefers a life of solitude.
You could then use each of those three key points to explain how the lawyer changes during his confinement, particularly using the letter he writes and contrasting that with his earlier actions in the story.
I hope you find this helpful in organizing your thoughts. Good luck!