Does anyone have any ideas as to how we could express the musical instrument "lyre"?

There's the {HurDagh} (n) "stringed instrument (general term)", {Supghew} (n) "type of stringed instrument", {leSpal} (n) "type of stringed instrument", and {tIngDagh} (n) "type of stringed instrument".

Does something of the above correspond to the lyre, or should I use the time-honored approach of writing *lyre*, and be done with it?

Well, a lyre is a HurDagh, so if you could write "my stringed instrument" and be satisfied with that generality, you're good to go.

We know the names of the three instruments you mention above, and we know little about them. The Supghew is "relatively small" and "the most commonly found." The leSpal is "midsize" and "fairly widely used," and the tIngDagh is "large" and "rarely heard except in conjunction with the performance of an opera."

Hol 'ampaS claims without source or evidence that a Supghew is like a ukulele, but I suspect whoever wrote that note was confusing the pun of the word Supghew with its actual meaning in Klingon.

The tIngDagh sounds almost exactly like a harp or a concert harp: large, and rarely heard (nowadays) except in large orchestral performances. The pun namesakes of Supghew and leSpal are clearly the ukulele and the guitar, but we cannot infer just from what's in KGT that these are the Klingon equivalents of these instruments.

A lyre is kinda-sorta like a harpHom, and a harp is kinda-sorta like a tIngDagh, so you might get away with calling a lyre a tIngDaghHom (maybe a tera' tIngDaghHom). But this is just potential resemblances through multiple stages, not a fact to stand by.

-- 
SuStel
http://trimboli.name