Lyrics does scroll when using audio regions. On each loop iteration the time is reset to the beginning of the loop. The time spend in the loop does not sum up. So if your song is only 15 seconds long but you would like to have lyrics for maybe a minute, looping audio regions is not really the best option for you. I would render the song in a length that accommodates all your lyrics.
What you suggest does not make sense in my opinion. For example if you exit a loop sooner or later than originally intended, your lyrics would be off.