"“My last supplication of all is this;..."See in text(Book the Second: The Golden Thread - Chapter XIII)
Though Sydney has been in love with Lucie since they met at Charles's trial (and though he came to hate Charles), he has finally come to accept the inevitable—that Lucie would never choose an alcoholic lout like Sydney. However, Sydney doesn't want to cut the couple out of his life; he wishes to continue a genuine friendship, though he has no intention of changing otherwise. He offers himself as a sort of sacrifice to Lucie, telling her that he will do anything for her or anyone she loves—as long as she remembers him as selfless and loyal.
"“I am the resurrection and the life.”..."See in text(Book the Third: The Track of a Storm - Chapter IX)
Sydney views his sacrifice as a sort of double resurrection: he will resurrect Charles from certain death while redeeming himself of his flaws. Sacrificing his life for Lucie's happiness is the only form of love Sydney can offer: he doesn't think he can be resurrected during his lifetime through reformation, so he opts for dying in the name of honor and loyalty.
"“It is a far, far better thing that I do than I have ever done; it is a far, far better rest that I go to than I have ever known.”..."See in text(Book the Third: The Track of a Storm - Chapter XV)
Sydney imagines Lucie having another child and naming it (if it's a boy) after Sydney because of his heroic sacrifice. Sydney has finally found a purpose for himself: trading places with Charles at the guillotine not only saves Charles's life, but also Sydney's life. Sacrificial death is his redemption from the sins of intemperance and laziness.
"ever known..."See in text(Book the Third: The Track of a Storm - Chapter XV)
Sydney Carton imagines a resurrection for himself in heaven and in the form of Lucie’s son. His sacrifice will place him in an honored position in the Manette family and erase his legacy as Mr. Stryver’s “jackal.”
