In Harper Lee's To Kill a Mockingbird, it is understandable that Dill might want Boo Radley to come out and visit with them to feel better because Dill is a lonely child himself—this is why he tells so many "tall tales" (lies)—so that he can get some attention.
It seems that Dill's mother has remarried and the fact that Dill is able to spend the summer in Maycomb indicates either that his mother has no one to care for him when he is out of school, or that it is difficult having him around and easier to send him away—especially in light of a marriage to someone not used to having kids around. Dill has lots of stories to tell, including some about his dad, but Scout is aware that he makes up a lot of what he says.
Additionally, with Dill's imagination, the idea of the mysterious Boo coming out to spend time with them appeals based on the plots and stories they make up: it's like something out of a mystery book. The children don't know it, but Boo would be extremely comfortable in their company, rather than that of adults. At the same time, they have built up such a frightening image of Boo based on the gossip they have heard, that it is hard to imagine how they would act if they all came face-to-face with him.
Dill's motivation, it would seem, is to provide companionship to someone he believes is as lonely as he is.