What is the purpose of cartons visit to lucie?

Carton comes to Lucie late one evening for a time of "confession" to her. He bemoans the fact that he has become such a low human being; he feels as if he can never achieve any kind of redemption. Lucie, being the kind and gentle soul that she is, assures him that he can become a more worthy person, especially to himself. He does confess his love for her when he says she is the "last dream of my soul" and vows by the end of their meeting that he would die for her if necessary.