Ellen McLain explained a bit about the creation of the Turret Opera at Anime Midwest 2011:
(watch from 1:00 to 4:55)
Video transcription starting from 3:30 up to 4:55...
When we were in the studio, I did all of the recording in a lot of different syllables.
You know... Doo-doo-doo, va-va-va, la-la-la... You know, different consonants and different vowel combinations.
And then Mike said: "Well, can you just make up some words?" And I said: "Sure!"
So I made up words in my very bad high-school Italian, because I studied Italian when I was in the high school.
And I have to say that Mike and I have decided that we are not going to divulge exactly what I said, because we love all the creativity.
On the Internet, the translations are close or not so close, but none of them have been absolutely correct.
But it was, because Mike Morasky told me in the recording session, he said: "This is the goodbye. This is the goodbye to the player. So, hence, this is the goodbye to Chell."
So I started making up words in Italian.
Maybe we will never know for sure what are the the correct, "official" lyrics, but we know they are Italian (or something that resembles Italian), and also that some unofficial translations got pretty close.
EDIT: I just noticed that Keaanu had posted a comment linking to Ellen McLain answering questions from Reddit:
5.Q) “What is the story behind the Turret opera song? Was this something you wanted to do with your opera background?”
5.A) The composer, Mike Morasky was the driving force behind the Turret Opera. He wrote all the music. He requested that I use my legit voice (operatic sound) on some of the takes. He chose the takes to use. He asked me to make up some words. So I did so in my bad Italian.
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