I would classify Lord of the Rings as literature because of its huge impact on fantasy. Its world building was a template for thousands of other works of fantasy.

I would also classify it as literature because of this: Literature doesn't need to involve extravagantly written prose. Sometimes the story is what matters.

Tell a great story, and you've become a master of literature.

IMO, C.S. Lewis was a better writer than Tolkien, and Salinger was better than both (although I preferred Franny and Zooey).

There are few writers who can be masters of both sides of the craft. Toni Morrison was able to, but she was a very rare gift to us all.