Take a story's temperature by studying its tone. Is it hopeful? Cynical? Snarky? Playful?
As The Lord of the Rings series progresses and we get involved in higher-stakes battles between good and evil, the tone of the storytelling itself changes. The Return of the King has the grandest, most sweeping language of the three books. Take, for example, Éomer's cry to his men when he realizes that Éowyn has been fighting the Witch-king of Angmar, the Lord of the Nazgûl:
"Éowyn, Éowyn!" he cried at last. "Éowyn, how come you here? What madness or devilry is this? Death, death, death! Death take us all!"
Then without taking counsel or waiting for the approach of the men of the City, he spurred headlong back to the front of the great host, and blew a horn, and cried aloud for the onset. Over the field rang his clear voice calling: "Death! Ride, ride to ruin and the world's ending!" (5.6.35-6)
Éomer's language to his sister—in spite of the fact that he is clearly freaking out—has an odd, old-fashioned grammatical structure. He says, "how come you here?" instead of "what are you doing here?" or "how did you get here?" Éomer's deliberately old-timey speech patterns give this whole scene the feel of an epic ballad, something like Beowulf or the Sagas of Iceland.
Beyond the old-fashioned use of language, the great armies fighting among each other and the constant sense of action and battle throughout the first book and a half of The Return of the King gives this novel a big sense of, well, bigness. That's why we say that the tone is grandiose. Even the characters who are usually more average and everyday in their observations and ideas—Merry and Pippin, we're looking at you—are getting caught up in battles against mountain trolls and Nazgûl. The scale of The Return of the King is huge, as Tolkien moves us from Dunharrow to Gondor to the Paths of the Dead to the Haven at Pelargir to Isengard, Fangorn, the Shire, and the Grey Havens. No wonder his language also has to grow grander and more serious. He has to find the words appropriate for expressing the ambition of his storytelling. This is a Big Book about Big Ideas, folks. So you'll have to pardon the Big Words.