I think it is pretty clear that Johnny's feelings for Dove have changed by the end of the novel. However, I don't think his feelings toward Lyte really have very much. At various times early in the novel, there is no doubt that Johnny looks down on Dove and bullies him around. He also hates Merchant Lyte.
By the end of the book, Johnny seems to have more respect for Dove or is at least kind to him. He does things like doing Dove's work for him so Dove can sleep (Chapter IX).
In Chapter XI, Johnny finds out that Merchant Lyte is his great-uncle. He does not react with revulsion like he might have before. Instead, he just kind of takes it in stride. This implies that he's okay with the idea of being related to Merchant Lyte. However, he's still not all that fond of Lyte, because when Lavinia says Lyte is the "best man who ever lived," Johnny "had his own opinion on that."
In the book "Johnny Tremain" the merchant Lyte had done Johnny a great injustice when he tricked him. After he is ill and Johnny has participated in the war, Johnny goes looking for Rab in the city. He runs into Lavina Lyte, his cousin. She tells him that her father had never meant to trick him and that he is going to sign a paper saying it was all a mistake. I don't really think that his feelings change that much because he doesn't say. I just think it is not that important to him any more. He has other things on his mind such as finding his friend and continuing assisting in the revolution.
Johnny's relationship with Dove changes through their experiences. Initially he has no trust in Dove. He witnesses Dove steal tea. Dove later becomes Paul Revere's horseman and cares for his horse. Dove gives Johnny needed information. On page 187 Chapter IX the book states that
"Johnny's feelings for Dove had changed."(187)
Johnny no longer likes it when the other boys make fun of Dove.