As the crowd celebrates Charles's conviction in the streets, John Barsad, who is escorting Charles back to his cell, lets Lucie her embrace her husband for the last time. Charles says farewell and asks her to kiss their daughter. Lucie tells him she feels that they will not be long separated and will meet in heaven.
Lucie has some kind of serene connection to the next world. If their love isn't possible in the world, it will be renewed in heaven. Note how well positioned Barsad is to smuggle Carton into Charles's cell.
Devastated, Dr. Manette tries to apologize to Charles. But Charles stops him, and instead thanks him, acknowledging all that Dr. Manette must have suffered to offer his own daughter back into the Evrémonde family he justifiably hates.
Like Dr. Manette, Charles also had a horrific secret past, of which he was unaware, come back to haunt him. He cannot escape the curse on his family.
Lucie faints. Carton carries her to a carriage and escorts her home. There, he instructs Dr. Manette to use any remaining influence to try to save Charles. Dr. Manette hurries away. However, once he's gone, Carton and Mr. Lorry confess they have no hope.
Carton is just distracting Dr. Manette; he knows that politics are no longer of any use. Something stronger is necessary to break the grip of fate, history, and the Revolution.
Lucie's daughter begs Carton to help. Carton embraces her and, before he leaves, kisses the unconscious Lucie and whispers, "A life you love."
As his farewell implies, Carton's goal is to give Lucie and her family a happy life. He is willing to sacrifice himself for that.