While Tolkien was fundamental to the development of the D&D rules, Lord of the Rings was just one of many influences on roleplaying games as a whole. Swords & Sorcery, other fantasy subgenres and even science-fiction were all thrown into the mix of those early games.
Just because it was cool in the eyes of the players and referees.
As for Tolkien the author and the Lord of the Rings rose in popularity through the late 60s and the 70s. However he didn't spawn much in the way of imitators. Far more popular among authors were the 1001 variants of swords & sorcery with a sprinkling of original works like Elric, Earthsea, the early Deryni novels and many of the novels of Appendix N of Gygax's DMG.
Then came Terry Brooks and the Sword of Shannara around 1977.
It didn't have much of literary impact. Many ripped it apart for being a pastiche of Tolkien. Even among gamers I never heard of anyone saying stuff from Shannara was really cool.
However Brooks did manage to break into the New York Times bestseller list. Something that no fantasy author including Tolkien managed to do.
My opinion of the book was that it was a fun and easy book to read. But not memorable in any particular way. I never followed up on the sequels after taking a stab at the Elfstones of Shannara, once was fine.
Since it was a big epic fantasy in the mode of Tolkien that cracked the NY Times list every fantasy imprint started putting out epic fantasies. Another early success was the Thomas Covenant series.
Despite the emphasis on the big epic the resulting market expansion brought in a lot of different styles of fantasy. Two of my group's favorites were the Guardian of the Flames series and Thieves World. My personal capstone of the era was Elisabeth's Moon's Deed of Paksenarrion series released in the late 80s.
After Shannara, Tolkien's style dominated the mass market for fantasy which had a lasting impact on RPGs. The most visible result was the release of Dragonlance.