I went and did some googling myself. Google suggested the word oliguria when I searched Oligoludia, which is some medical term for low urine output... I figured there must be some Latin or Greek origin, and oligo means small or little. I looked to see if ludia was something, and it says that it means beautiful or noble one. So small beautiful one or something. Referring to some precious and sublime thing probably. It kind of gives me the same vibe as the Sublime Sword of the Creator from 3Hs.
Then with Lyration being similar with lyrate, it doesn't literally have be lyre-like in appearance, but in function if that makes sense. So the invigorating sound is what boost the engage meter of allies. Engage was TMS 2 all along. Even more digging on the significance of the lyre in Greek history, it relates to Apollo the god of music and the Sun. Also Hermes the messenger god. On the Wikipedia page of Lyre it says that the lyre could have exited in neighboring countries to Greece including what was Lydia. The region of Lydia can also be called Ludia. So maybe that's the relation with Oligoludia.
I'm just parsing a bunch of random information so idk. This seems to be a similar case as the Ichival or Yewfelle, where IS just made up a weapon.