Another theme that they share is the dangers of technology. The telescreens of 1984 and the palantíri of Lord of the Rings have a lot in common - both are subject to manipulation that can require a great deal of will to see through.
>"[Saruman] is plotting to become a Power. He has a mind of metal and wheels; and he does not care for growing things, except as far as they serve him for the moment" (Tolkien)
The phrase "a mind of metal and wheels" has always stuck with me as a pejorative; this is in contrast with modern phrases like, "He's a machine!" said in a positive way. The mind of metal and wheels is transactional, utilitarian, devoid of sentiment. It would be more like a natural process than a person, if not for ego.
I basically like where you are going with this, but wonder why you then say that a transactional/utilitarian process is like a natural process?
Nature as Tolkien seemed to understand it would be anything but transactional and utilitarian.
Because it's impersonal. There's no chooser, it's like the planets zooming around the sun. It is a clockwork that we can understand, but not affect. It doesn't know or care about us - we happen to live on one of the cogs, but the planetary machine would function smoothly with or without any life on the 3rd planet.
Capitalism is much like this. Institutions of a certain size can be like this. Being stuck in a machine is the context of "Howl" by Allen Ginsberg [0]. It is also the subtext of the remarkable "Blame!" anime, a drama that takes place among humans and robots that live as vermin in an automated city that takes little notice of them [1]. Or a more traditional treatment, with a very powerful Mech civilization dominating humans in Benford's Great Sky Rivier [2].
0 - https://www.poetryfoundation.org/poems/49303/howl