[Lalaith]

I think the only Noldo we actually know of in Lorien is Galadriel herself. Celeborn was Sindarin, and their people were mostly a mix of Sindarin and Silvan. Legolas calls himself "a kinsman here" if you remember, that is because he too is a Sindarin. But I think the people his father ruled over were
Oh btw, Frodo did not understand Quenya at the time of LoTR. (Although I expect he learnt it subsequently.)
Queyna "Elvish Latin" and was in the Third Age rarely spoken on Middle Earth, is the language Galadriel speaks as they bid farewell to Lorien.
In the LotR appendices, the section "Of the Elves" explains that Frodo made an error thinking the elves of Lorien spoke another language. As Durelen's source says, it was simply Sindarin with an accent he didn't understand.
As we've discovered, the Avari question is very problematic, particularly given all the revisions the Professor made during the course of his long life.
In one source I read (I'll try to find an internet link in a sec) the Noldo Avari didn't like their posh Aman cousins. Also all the Avari felt betrayed by the Eldar, and called themselves "the Deserted."
Lindil, I'd be very interested to see what research you can find.