Hivemind
We're Touched
Well, I'm not sure that LoTR should even be considered "high fantasy". My understanding is that high fantasy is set in an alternate, fictional, world- like Game of Thrones. "Low fantasy" (actually a thing apparently) is set on earth, in the real world. LoTR is set on Earth, roughly 4000 BC. I don't think the phrase "high fantasy" existed at the time he wrote it, but I suspect Tolkein would object to the term (he objected to a lot of things people said about his work). I realize this is kind of a semantic argument but I would call Tolkein's work fictional mythology, or even fictional folk tales. Much more in line with things like the Nibelungenlied than with Game of Thrones or other "high fantasy".
Sorry, I'll get off my soapbox now.
More broadly speaking:
High Fantasy = Fantastic creatures (dragons, elves, faeries) & settings (typically an original world with its own "rules") in which there is a heroic quest and/or world-defining battles between good & evil
Low Fantasy = Fantastic elements introduced to a "realistic" setting (often a real world setting), in which there is grit, realism, and/or moral quandaries. Scales may not be as high.
The setting is certainly one distinguishing factor, but not the only one. And Arda certainly fits into a High Fantasy setting, as it is an invented world with its own rules. Just because Tolkein envisioned it as an imagined pre-history doesn't really change that it's a high fantasy setting. It's still a world that comes from Tolkein's imagination, with its own creation story, it's own internal logic/magical system/nature, and it's own set of imagined inhabitants. It has even less connection to the real world than books like the Oz series or the Chronicles of Narnia, both of which contain imagined parallel worlds but feature characters taken from our real world in the author's present day.
Things like Game of Thrones blend both High Fantasy (dragons, magic, invented worlds) with Low Fantasy (politics & soap opera drama, grounded/gritty combat, nihilistic characters, moral quandaries).