Dill lies about his father because he doesn't know him. He also lies about a lot of other things, a quality which he shares with Mayella. He probably lies because he wants to fit in since he isn't from the South but is from Mississippi. Although he is readily accepted into the town because he is a child, he may be lying to create a place for himself in the society. Because he is technically an outsider, Dill adds adventure and intrigue to the childrens' lives.
