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.
Best Answer
Here are the screenshots of the rooms you see on the elevator ride up to the surface at the end of Portal 2. Apologies beforehand as some of the screenshots are a little fuzzy, but the descriptions should help clarify any details that may be unclear.
A row of four turrets initially targeting the player who then go on to sing
Two turrets singing
Four partially assembled/defective turrets
Three turrets at 90 degree angles (apparently mis-assembled)
Four turrets staring at the Aperture Science Weighted Storage Cube
Four turrets surrounding another cube staring at the player
Eight turrets facing the player in two rows of four
Two turrets who appear to be behind a ruptured transportation tunnel (would explain the angle of the turret to the left) or possibly tangled in roots (see comments)
A large room filled with an assembly of turrets, in the spotlight is the 'tenor' turret and in the background is the oversized 'animal king' turret