I must answer, because I am a Tolkien fan and also saw Narnia. I think that without Tolkien Narnia wouldn't have been such a success, like most of fantasy stories which came after Lord of the Rings. I guess Tolkien set a stone. But that is only my subjective estimation. ...
Like: without Star Wars Science Fiction wouldn't have become so popular.
I'm reluctant to say that Tolkien alone made the genre of fantasy popular. Fantasy, or "fairy stories" as Tolkien likes to call it (see Tolkien's essay), were very popular long before Tolkien wrote The Lord of the Rings or even The Hobbit. Tolkien was heavily influenced by George MacDonald's fairy tales, which were written in the nineteenth century.
I'm also reluctant to say Tolkien's work made The Chronicles of Narnia popular. The Lion, the Witch, and the Wardrobe (1950), Prince Caspian (1951), The Voyage of the Dawn Treader (1952) and The Silver Chair (1953) were all published, and became wildly successful, before The Lord of the Rings was released in 1954. Tolkien and Lewis' stories and writing style, as well as their worlds, are also so different, I don't think it is fair to compare them on the same scale. Both Tolkien and Lewis are brilliant worldbuilders and storytellers, and I think each must be appreciated on their own, although we, as readers, are allowed to have our favourites. :)
Totally:) - I wanted to point out that those writers who have made it into the top are great influencers of what comes after them. I was watching from above and that was the first thought popped into my head as I read your post.
For the non educated reader - like me - it seems to be like it was the case I mentioned. I guess I represent the mass for I did not read Lewis but only saw the movie.
So it is good to be corrected.
I appreciate art wherever it is folding up in front of me.
Which of the Narnia movies did you see? What did you think of them? The Lion, the Witch, and the Wardrobe follows the events of the book pretty accurately but Prince Caspian and The Voyage of the Dawn Treader are only loosely based on the books.