What she's singing appears to be a Macross Frontier song known as Lion. The lyrics at this point (2nd paragraph) are pretty much just straight up "I want to survive" and it seems Mystia wasn't expecting it to be quite so context-sensitive.

I'll leave it up to someone more experienced whether to translate it directly or not, but I'll note that an excellent way to localise the joke might be to use I Will Survive instead. They even both have a repeated line at an iconic part of the song.