The good prof was always approaching it from the twin p-o-v of language & of story, I think. He wasn't a musician. He could poet, for sure, but whether he had a notion of how music should have sounded... I may be wrong, but I don't think he had a particular notion, and I am fairly sure that I did read something once, etc!

The lyre isn't a well known instrument and, when it is recognised, tends to be associated with Apollo & the Greeks (the A/S version is quite different in form, but doesn't have many more strings & is not much more polyphonic). Which makes it earlier & simpler. In general, early music, where instruments are concerned, tends to be relatively uncomplex, because the instruments are. The Hobbit isn't quite 'canon' in comparison with the rest of the work. Clarinets & flutes (I've always assumed we're taking orchestral flutes, not the earlier, simpler equivalents) and the rest of it... We're now in Shire / Sarehole territory - JRR's presentation of an idyllic 19thC English village.

The reality of Arda is that it is several hundred years simpler & so are the instruments. Harps would exist, but they wouldn't be 23-string clarsachs, never mind modern orchestral jobbies. 15-18 strings maybe, at most, and gut strung, not wire, so quieter, and you can expect the music to be less technically complex. If you treat Arda as being early medieval / late Dark Age, you can expect to have pipes of some sort, harps ditto & drums. Some sort or horns and, possibly, trumpets (serpent or bugle style, not the orchestral type). Woodwinds would be shawm-type instruments. There might be lute style things, but only for quiet, relatively private gatherings. And rebecs. Not violins, viols, or fiddles. Rebecs look somewhat similar, but they are not the same family of instrument.

What you wouldn't have is any sort of guitar or modern orchestral instrument. Apologies if this is thread drift, but then David started the thread & is engaged in any drift, so I blame him! ;-)