I don't know, Imladris.
To be a mythology, would that not have to be a belief system that is no longer believed? Like the Greek and Roman mythologies were once believed in as true religions but no one today worships Jupiter, Jove, Hera, Athena, etc etc.
So, that would make LOTR something no one really believes in any more, ie, something passing away into the mists of history, ignored and discredited. Like the elves?
Doesn't sound like it to me.