Dill's relationship with his parents is complicated. While never directly stated, there is the suggestion of divorce and possible boyfriends. Of course, with Dill's overactive imagination, one can not be quite sure where reality begins and ends in his tales. It could be that his father is very much a part of his life- just a part Dill wants to forget.
Every time Dill comes to visit, he claims to have a new father. His fathers' occupations include everything from "a lawyer like Atticus, but much younger" to the "president of the L&N railroad." He does state at one point that his father is not around, and so he may deal with his issues of abandonment and neglect through fantasies. When he runs away to Finches, just before the trial begins, he says he had "been bound in chains and left to die in the basement...by his new father, who disliked him". Later he admits he simply ran away. Whatever the situation, it is clear Dill's real father is not providing his son with the care and love he needs.