In my opinion, Dill does this because of the relationship (or lack thereof) with his father in real life. In real life, Dill's parents do not seem to have much time for him. They love him, but they do not spend time with him.
Because of this, you can see where he might want to compensate. So he makes up all these stories about him and his father. In the stories, they do all sorts of things together. This makes it seem as if his dad really has a lot of time for him even though in real life he does not.
Dill feels inadequate about the fact that he does not have a loving father, which is why he tells numerous lies to Jem and Scout. Throughout the novel, Dill is a creative child who is extremely lonely. Scout also mentions that Dill tells the biggest lies. Dill doesn't want to feel inferior or different from Jem and Scout and tells them lies about his father to make himself feel better. Dill lies to Jem and Scout by telling them that his father is very tall, has a long black beard, and is the president of L & N Railroad. Dill is both embarrassed and hurt about his family situation. He also wishes to impress Jem and Scout and resorts to storytelling as way to get their attention. Dill's stories allow him the opportunity to imagine and believe that he does have a loving father like Atticus.
Dill appears to be a very lonely boy. He first meets Jem and Scout when he visits his grandmother and elderly relatives. He is young and in need of friendship. His parents are separated and he has been moved about. He has the opportunity to observe Scout, Jem's, and Atticus' relationship. His relationship is lacking the closeness that he desires. In order to compensate for that which he desires but does not have, Dill makes up stories to fill in his lonely gaps.