Lucie is a foil to Madame Defarge in A Tale of Two Cities. In other words, she plays an opposite role to Madame Defarge and helps the reader to understand the character of Defarge better.
Lucie is the epitome of goodness and peace; in contrast, Madame Defarge represents the hatred and chaos of the French Revolution. Lucie's role is to restore life and hope to her father, to Charles Darnay, and even to Sydney Carton, who believes himself beyond hope. In contrast, Madame Defarge is the destroyer of peace, even leading the women in the storming of the Bastille, and she tries to destroy the lives of the Manettes, as well as all the other people who may have been associated with the nobles in France.