Bring on the tough stuff - there’s not just one right answer.
Just as The Fellowship of the Ring starts with an introduction, The Return of the King ends with appendices (collections of notes and historical details drawn from Tolkien's invented mythology for Middle-earth). It's as though TheLord of the Rings is a piece of linguistic and historical scholarship, like Tolkien's own edition of the Middle English anonymous narrative poem SirGawain and the Green Knight(published in 1925). But The Return of the King is obviously not a recovered medieval manuscript or anything. Nope, this is a standard, 20th-century piece of fiction. So we have to ask: why does Tolkien try to imitate the appearance of a scholarly work in his fantasy trilogy? How do the appendices change your reading of the series as a whole? What would The Return of the King be like without appendices?
By the end of The Return of the King, Frodo (now the most elf-like hobbit ever) leaves the Shire to decent hobbits like Sam, while the elves leave Middle-earth to decent men like Aragorn. How would the whole moral impact of The Return of the King change if Frodo and the elves had not sailed into the West? What if they stuck around in Middle-earth even after the fall of Sauron? Would you prefer that ending? Why or why not? And what might it mean thematically?
Why does Tolkien include Éowyn's unrequited love for Aragorn in the novel at all? What does it add to The Return of the King? How would the novel change without this subplot? Why does Éowyn's romance with Faramir make it into the main part of The Return of the King while Aragorn and Arwen's love story gets stuck in the appendices? And what role does romance play in the characterizations of Éowyn, Aragorn, Faramir, and Arwen?
In a letter, Tolkien comments that Frodo expects to die at the top of Mount Doom after the Ring has been destroyed: [Frodo] appears at first to have had no sense of guilt (III 224-5); he was restored to sanity and peace. But then he thought that he had given his life in sacrifice: he expected to die very soon. But he did not, and one can observe the disquiet growing in him. (Source, pg. 327.)
Because Frodo doesn't die—because he has to live on with his horrible memories of the Ring and his last struggle with Gollum—he starts to get sick back in the Shire. Would The Return of the King change very much if Frodo had died at Mount Doom? How would Frodo's death alter the rest of the book? Would Frodo dying at Mount Doom be a more or less effective conclusion than the one Tolkien actually wrote for The Return of the King? Why?
Legolas and Gimli both seem to disappear over the course of The Return of the King. They remain friends with Aragorn, but they don't have the same kind of strong narrative arc that the hobbits or the humans of the novel enjoy. Why not? How would The Return of the King be different if we followed Gimli or Legolas's perspective after the fall of Sauron?
Even now, at the end of TheLord of the Rings cycle, we still don't really know why Sauron is so evil in the first place. Why do you think Tolkien chooses to leave out that little tidbit? Would the story change if we got a bit more of Sauron's history?