A fantastic article. The Lord of the Rings is about many things - the battle between good versus evil (not just external evil, but the evil within oneself), courage, friendship, war, the environment, faith (inherently, even though Tolkien wasn't intentionally allegorical), the melancholy of the end of an era, growing up, and, yes, love. Not just romantic love.
I would strongly echo other commenters who urge reading the books. Regarding the themes you discuss here, the leisurely wrap-up in the final chapters feature several, move-me-to-tears segments. This one, for instance, from Gimli in the chapter Many Partings, after the crowning of Aragorn, the weddings of Aragorn and Arwen, and of Faramir and Eowyn, and after the ride to Edoras (Aragorn and the others ride that far with the hobbits, Gandalf, etc). At last, it is time for our friends to say farewell.
“We will send word when we may, and some of us may yet meet at times; but I fear that we shall not all be gathered together ever again.”
After Gimli's all-too-relatable farewell to comrades who have been through much together, there's an absolutely stunning, deeply melancholy moment when Aragon sits on his horse with his knights, watching the hobbits depart, and pays them this extraordinary tribute. I wish this vivid image had found its way into the films. It has me blubbing like an idiot whenever I read:
"With that they parted, and it was then the time of sunset; and when after a while they turned and looked back, they saw the King of the West sitting upon his horse with his knights about him; and the falling Sun shone upon them and made all their harness to gleam like red gold, and the white mantle of Aragorn was turned to a flame. Then Aragorn took the green stone and held it up, and there came a green fire from his hand."
In the film, they went with "My friends, you bow to no one" instead, which is also powerfully moving, I grant you.