When the original books were published in England in the 1950s, they were reviewed as serious literature because they were written by an Oxford don with serious credentials and published by George Allen & Unwin, a serious firm. That it was fantasy was not a barrier at the time. Fantasy was considered to be a literary genre quite separate from science fiction, which was a pulp magazine illiteracy. Serious writers, like those in the Inklings, encouraged fantasy reading and writing.
Therefore LotR was received as serious literature and treated appropriately, i.e. reviewers praised and belittled it as they would any other novel set before them. In broad terms, the book was looked at more favorably in England than in America, where fantasy did not have the same literary tradition and science fiction had suddenly gained some respectability. (The New York Times Book Review set up a semi-regular science fiction review column starting in 1950, something it doesn’t have today.)
The hardback edition made Tolkien money but wasn’t in any sense a bestseller. Both fantasy and science fiction lost their luster by the end of the 1950s. Unexpectedly, a new generation of writers were met by the rise of paperback firms willing to publish original f&sf novels instead of only reprints and the field rose as suddenly as it had in 1950. Ace Books in early 1965 tried to use a loophole to reprint LotR and drew so much opposition that it withdrew the books. Ballantine negotiated for the official edition and put it out in late 1965. That edition had the iconic covers which fit together and made one larger scene, printed as a poster for every dorm room. It was that Ballantine edition that sold so many millions that Henry Beard and Doug Kenney of the Harvard Lampoon could parody it as Bored of the Rings in 1969 and sell a million copies on its own. When a parody sells a million, the original has to be omnipresent. This publication history page for the first book alone is mindboggling, and it’s just the U.S., U.K., and Canda.
The current literary assessment is very much like the original one in 1954. You either worship Tolkien and think that he wrote one of the great novels of the 20th century or you don’t get what they see in him and trot out a long litany of faults.