In "The Swimmer," does Neddy gain a sense of freedom after his journey on the Lucinda?
He does not gain a sense of freedom. In fact, he is trapped. At the end of the story, Neddy is trapped at the end of his journey. Not only is he locked out of his house, but his house has also been foreclosed upon. His daughters are gone. His wife is back at the start of his journey. The cold night is upon him. I am actually hard pressed, outside of the works of Shakespeare or Flannery O'Connor, to think of a more pessimistic end to a piece of literature.
At the story's conclusion, the reader is aware of how ridiculous Neddy really is. Initially, he seems youthful and even heroic as he sets out on his journey. However, as his swim progresses, we learn that appearance is not reality. Neddy is not as young nor heroic as we are led to believe. With every stop on the Lucinda river, we learn something more distressing about him, whether it is that his memory seems to be slipping (he doesn't recall a good friend having surgery or why another couple has moved and left their stable seemingly abandoned), he seems to have had financial trouble, and even his former mistress rebuffs him.
However, while the reader realizes that Neddy is not as heroic as he initially appears, there seems to be little evidence that Neddy realizes this. Perhaps, that last image of him locked out of his own vacant home could be seen as his epiphany; however, there is little proof of that.
Instead, the lasting image is that of not a freeman but of a man trapped by fate.