Madame Defarge is deeply traumatized by the abuse her family suffered at the hands of the aristocratic Marquis St. Evrémonde. He raped her sister, her father died of sorrow over this, and her brother was killed trying to get revenge for the rape. This has filled Madame Defarge with a deep hatred of the whole aristocracy, particularly the St. Evrémonde family. She is utterly, obsessively, and ruthlessly bent on revenge.
Madame Defarge assigns guilt to Darnay, Lucie, and little Lucie because they are related to the Marquis St. Evrémonde: Darnay by blood and Lucie through marriage. The three are innocent of wrongdoing, but Madame Defarge wants to wipe out anyone associated with the Evrémondes. As the narrator states,
imbued from her childhood with a brooding sense of wrong, and an inveterate hatred of a class, opportunity had developed her into a tigress.
Even though Lucie is only tenuously connected to the Evrémondes, Madame Defarge still considers her fair "prey" who should be one of the many made to pay for what has happened to her family. She memorizes Lucie's face and that of her family members so she will be ready when the opportunity to strike arises.
Through Madame Defarge, Dickens shows how revolutionary zeal and class hatred can go overboard and become the justification for an indiscriminate bloodbath. Madame Defarge's corrosive hate and resentment have made her cold and inhuman.