Like many children, Dill creates a larger-than-life father to make up for the obvious deficiences that the man exhibits. Throughout Harper Lee's novel To Kill a Mockingbird, Dill displays a knack for storytelling, and the tales about his father are among the biggest whoppers he tells. No doubt Dill feels neglected by both parents, who ship him off to his Aunt Rachel in Maycomb each summer instead of using the free time to spend with him as most parents would. Instead of admitting the awful truth to Jem and Scout, Dill creates fantastic stories that make the Finch children admire and envy him--at least some of the time.
... I asked Dill where his father was: "You ain't said anything about him."
"I haven't got one."
"Is he dead?"
"Then if he's not dead, you've got one, haven't you?"
Dill blushed and Jem told me to hush, a sure sign that Dill had been studied and found acceptable.
Dill's fascination with Boo Radley only intensified Jem and Scout's own curiosity about Maycomb's mysterious ghoul. When he next returned, he now had a father
...taller than ours [with] a black beard (pointed) and was president of the L & N Railroad.
But by now, Jem and Scout knew him well:
"I helped the engineer for a while," said Dill, yawning.
"In a pig's ear you did, Dill. Hush," said Jem. "What'll we play today?"
Still later, Dill runs away from home, where Scout discovers him under her bed. Dill entertains his obviously enthralled pals with one of his greatest stories about
having been bound in chains and left to die in the basement by his new father, who disliked him...
But Scout suspected that no one could hate such a lovable fellow as Dill:
... "I said why'd you run off? Was he really hateful like you said?
"Naw... they just wasn't interested in me."
Scout realized one big difference between Atticus and Dill's father: Atticus needed Scout. Dill believed his parents didn't need him. Their serious talk turned to Boo Radley once again, and Dill philosophized about why Boo had never run away.
"Maybe he doesn't have anywhere to run off to..."
Dill's motivation for lying is that his fantasy world is much better than the real one in which he lives.
Dill, in part, shows that sometimes things just aren't the way that they seem. Some homes aren't places where children want to be. Jem and Scout see their home as nearly idyllic, even though Scout has some questions about the way Atticus does things. Initially, she can't figure out why Dill would run away from home.
The reason is that his own world he made up is much better than the real world he lives in. Dill's real family is horrible to him and his step dad locked him in the basement. Somehow Dill was able to escape, and he trusts the Finches more then his own family because they truly care about him.