What does Doodle lie about in "The Scarlet Ibis," and what does he picture his perfect future to be?

Brother, the narrator of the story, says that Doodle's lies are twice as crazy as his, but Doodle's "lies" are not really untruths; they are imaginary stories of how he wishes life could be.  All of his stories include "birds" and people who can fly.  Obviously, Doodle wishes that getting around was not so difficult, and the wings are a solution to his pain and efforts that he encounters when learning to walk and run.

When Doodle and Brother discuss their future, they talk about living out near the swamp with swamp birds as their chickens.  Even in this "realistic" story, Doodle wants them to be able to

"swing through the cypresses on the rope vines,"

negating the need for him to walk or touch the ground.