What are some proofs Carton loved Lucie Manette in "Tale of Two Cities", other than the sacrificing of his own life?
The first time Sydney Carton sees Lucie Manette is in the courtroom during the trial of Charles Darnay. Although his demeanor does not indicate interest, he watches her carefully, and is "the first to see it" when she begins to collapse upon her father's breast. He then subtly directs the officer of the court to help her (Book 2, Chapter 3).
After Darnay's release, Carton accompanies him to a tavern, where he sardonically brings up the subject of Miss Manette. Carton has noticed the way Lucie looks at Darnay, and is jealous and angry, although his wrath is directed mostly towards himself. Carton knows that although he and Darnay share a resemblance, they are nothing alike. He realizes that Darnay is everything that he himself could have been, and that if he had not chosen the path of disrepute, Lucie might look at him as she looks at Darnay (Book 2, Chapter 4).
The clearest proof of Carton's feelings for Lucie before he sacrifices his life for her is his behavior in Book 2, Chapter 13. In this chapter, he "haunts (the) neighborhood" of Doctor Manette, and one day finds the courage to seek audience with Lucie and declare his love for her. Carton knows Lucie cannot love someone as degenerate as himself, but he tells her that she has "inspired" him to at least consider the possibility of reform. In a clear statement of foreshadowing, Carton tells Lucie he will do anything he can to make her happy, even "give his life, to keep a life (she) love(s) beside (her)".