Lucie apologizes to her father because she is marrying Charles, and she does not want leave him alone.
Lucie was separated from her father for most of her life, and at this point in her life she wants to marry the man she loves but she feels torn between her duty to her father and her commitment to the love of her life.
But, if my life were not to be still consecrated to you, or if my marriage were so arranged as that it would part us, even by the length of a few of these streets, I should be more unhappy and self-reproachful now than I can tell you. (ch 17)
Dr. Manette tells Lucie not to worry about it. He wants her to be happy. He understands what it means to be in love, and he is happy for her. He wants her to live a full life. His happiness was taken from him before, and he does not want the same thing to happen to her.
Lucie is not fully aware of the situation. She does not know that her future husband’s family is responsible for her father’s imprisonment. Charles is an honorable man though, and he makes sure that Dr. Manette knows. Dr. Manette still wants her to be happy though. He sacrifices his own mental well-being for her, knowing what the news will do to him. He does relapse, but only while they are away.