Given that I just published an entire essay on Tolkien and rhetoric in JTR, I was a bit surprised to recently discover an article on just that topic. (Almost) The piece is "Is Tolkien a Renaissance Man?" by Tanya Caroline Wood, an essay in Tolkien and His Literary Resonances, edited by Clark and Timmons. Although admitting that there's no evidence that Tolkien ever read Sidney's Defense of Poesy, she does a hardcore rhetorical comparison between Sidney's essay and Tolkien's "On Fairy-stories."
Basically, both pieces mix the genres of encomium (which praises and elevates its subject) with the defense (vindicates an accused subject). The rest of the essay simply pinpoints mutual uses of classical rhetorical devices such as refutatio. There's no real "so what?" answer, and the piece never rises above bare comparison, but I was simply intrigued that there have been attempts to link Tolkien to classical (or, in this case, Renaissance) rhetoric, however misguided.