It is frustrating to search for exact Tolkien quotes, as the movie quotes pop up far more frequently than the book originals. You have to dig down a bit to find what Tolkien wrote two generations ago. I often resort to gabbing my own copies and searching out the words by hand. The lesser commodity value is in wider circulation.
I wondered years ago if the LOTR movies would push out the reading of the books, as they are in a more easily-digestible form. What Peter Jackson produced visually was far superior to anything in my imagination. (It is a notable weakness of my reading, likely at brain level, that I do not picture things well, and thus have little interest in books with much description. Just give me the general idea, thanks.) Yet he told a different story than Tolkien did. The original was much more focused on the ability of seemingly insignificant actors to do great things, while the movie - following the rules of its own art - had the camera on Aragorn and Gandalf much more. This was a matter of degree, not an entirety, to be sure, yet it does undermine the main point of the original more than a little.
The Lord of the Rings, book version, is no longer part of popular culture. It belongs to another era now, and I suspect most of its reading is rereading. The same is true for Lewis's Narnian chronicles. The few movies have cemented rather than prevented that. All of Lewis's writing now belongs to previous eras, more likely two generations previous than one. That both writers have enjoyed persistence is not quite the same thing, though I suppose one could reasonably claim they remained alive in a popular subculture until recently. Spiritually, a popular subculture is as dangerous as the popular culture or even more, as it has the potential to drag snobbery along with it. But for the more basic definition, "popular" has to track with actual popularity.
Nor is it a valid argument that they remain current because both can be read with profit today, as both authors would assure you with a chuckle. They were both nourished almost entirely on authors long dead and far removed, as invisible to their popular culture as to ours.
I think the same thing has happened with the children's classics with primarily female audiences. Does anyone read Little Women, Anne of Green Gables, or Little House in the Big Woods anymore? Were the movies and TV series a brief rescue or a final shove through the door from the present to the past? In the 1990s I know that such books were still being read, as they showed up in the voting for The Great Stone Face award, given in NH every year for most popular book. (Judy Blume, infuriatingly, won year after year.) In the 2020s they are likely still being bought and given to girls for their birthdays, yet I don't know there are actually many eyes on the page.