In To Kill a Mockingbird, what do Dill's lies about his father add to the children's lives?
I will answer this question, because you can only ask one question at a time. Dill lies because he desperately wants to have a real family. Dill's father left, and it deeply affected him. Dill has a mother and no father, and the Finch children have a father and no mother. It is natural that the three children would find each other, since they are close in age and all similarly inquisitive and intelligent.
Scout and Jem know that Dill is making up everything he says about his father, and he knows that they know. The descriptions of his father are just part of the vivid fantasy life that all three children inhibit when Dill is in town.
For the narrative, Dill accomplishes a few things. First of all, he allows the children to explore Boo Radley's story because they introduce Dill to it. Second, he provides the children with opportunities to move the story along, including the night Jem left his pants at the Radley's house and during the trial. Dill's situation also adds to the theme of family explored throughout the book, because Dill's story line involves another unhappy family. When Dill's mother remarries, Dill feels left out and unloved, so he is able to return to the Finches, his true family.