It occurred to me earlier that in the song “Birdhouse In Your Soul” by They Might Be Giants, they make a reference that I was unfamiliar with : The Longines Symphonette.
And, of course, in “Ramble On” by Led Zeppelin, there’s the part where he talks about Mordor and Gollum. Not really sure how that relates to the actual book series, as I can’t place what character Robert Plant is supposed to be. I imagine that it’s more of a “it was the 60s, and everyone thought they were Hobbits or whatever.” But I can’t think of another mainstream/non-novelty song that refers to the saga.
What else? There must be hundreds I’m not thinking of.
“The Wizard” by Black Sabbath is about Gandalf, and I don’t know if you’d consider Blind Guardian mainstream, but they have a number of Tolkien-themed songs in their catalogue, with “Time Stands Still at the Iron Hill”, about Fingolfin’s duel with Morgoth, being a favorite of mine.
Some of the musicians “performing” on the Bonzo Dog Band’s “The Intro and the Outro” was pretty obscure to Americans at the time and are even more so now: Val Doonican, Garner Ted Armstrong, Billy Butlin, Lord Snooty (UK comic character), Franklyn McCormick, et. al. Even a few that were well known at the time have faded into obscurity.
And speaking of Genesis songs, “Broadway Melody of 1974” from The Lamb Lies Down On Broadway throws out references to Howard Hughes, Groucho Marx, and Lenny Bruce, but I had to look up who Caryl Chessman was. https://en.wikipedia.org/wiki/Caryl_Chessman
The Cult has a song called “Aphrodisiac Jacket” which includes the line “plastic fantastic lobster telephone.” This sounds pretty nonsensical but they’re references to a couple of art pieces by Salvador Dali: Aphrodisiac Dinner Jacket and Lobster Telephone