I was reading volume 2 of Green Lanterns (DC Rebirth [the series about Jessica Cruz and Simon Baz]) and noticed that, when he was in compassion mode (the spoiler is just the antagonist of the arc, just want to be cautious that this great series isn't spoiled for anyone),
"...the language of the Indigo Lanterns" — Cosmic Cotton
Based on that, I would think that the Red Lanterns, Orange Lanterns, Yellow Lanterns, etc. would likely all have their own languages. However, I was just thinking that they might not all have their own languages and could maybe just use normal ones, because the alien Green Lanterns appearing at the end of the volume spoke in English to Jessica and Simon, without any special formatting or editors notes suggesting it was something else or translated by their rings. Therefore, my question is: Does each color of Lantern have its own language?