Why does Apollo play a lyre?

It seems like a simple question but mum's the word online and even Wikipedia doesn't help although it does touch on the iconic lyre in its current draft of the Apollo article. To me, it's most likely that the deity of the sun isn't given a stringed lyre due to anything more elaborate than a word pun in some forgotten tongue. Which one, when, and in what way are the remaining questions.

In fact, the ultimate source of the word 'lyre' is still a riddle. The etymology of Classical Greek λύρα, from whence the English word, is uncertain but most often suspected to originate from a non-IE language, most probably Minoan. Note that the word dates back to Mycenaean, as attested in Linear B ru-ra-ta-e = *lūrātāe '(two) lyrists [dl.]' so it could very well be a borrowed word from the Minoan language. So I hypothesize a Minoan form *lura 'lyre' as the most credible source.

Coincidentally I've already been interpreting lursθ in the Lead of Magliano as a proper intransitive participle of a stative verb luras 'to be bright'. Within its context, Tins Lursθ would be the genitive of an epithet meaning 'Shining Sun' pointing to the highmost one, Tinia. Inscription TLE 747 also attests to lursl, a type-II genitive of its corresponding bare deverbal noun, lurs, which would then imply 'light'. Since -as- seems to be a fairly productive derivational suffix in Etruscan verbs (possibly a stative marker) I anticipate a more active root, *lur- 'to sparkle, to shine', at its base.

This latest revelation has got me wondering if there is a connection with this sun-lyre motif. Given both *lura 'lyre' and *lura- 'to sparkle', there would be natural temptation to use the 'lyre' as a creative solar symbolism. Of course, I still need to investigate this further and make sure that these translations are solid but it's one tempting thought that has me itching for more data.