What is the life lesson in the story "The Third Wish" by Joan Aiken?

Two possible answers to your question come immediately to mind.  When Mr. Peters uses his second wish to turn Leita back into a swan, the old King comes to mock him; Mr. Peters serenely explains that “human beings and swans are better in their own shapes.”  Here we see one moral of the story:  you cannot turn someone into something he or she is not. If a person’s natural personality is suppressed, or if they are forced into a form that doesn’t suit them, as Leita was changed from a swan into a human being, then the person will have lost a key part of themselves, and will suffer all the more for it.  It was a very kind and selfless thing Mr. Peters did when he turned Leita back into a swan, and with her in her original form, they were both able to express themselves and their devotion to each other in a manner that made sense to them.  We learn that  “As Mr. Peters grew old, everyone wondered at his contentment.” He and Leita did not lose much by the compromise, and were instead able both to be happy. 

There were people in the community who wondered why Mr. Peters didn’t just wish for another wife after letting Leita go, to which he replies, “I’ve learned that even if your wishes are granted, they don’t always better you.”  Here is another lesson – sometimes that for which we long the most is not that which we need.  Or, when we achieve a goal or a desire is fulfilled, the effects we imagined are different from the reality of the situation.  And when this happens, we cannot be afraid to do what will ultimately make us happy – abandoning the thing we have earned.  If others suffer because of something we achieve, or if we ourselves are suffering, we must be humble enough to recognize the right path, and let go of our wishes if it turns out they are toxic, no matter our initial intentions.