I doubt you can do it in an automated way. Well, it might be possible somehow, but some of the lines wouldn't be right on some songs. The length of lines varies song to song.

This is of no help but as I started typing lyric sheets years ago, I made the font the largest it could possibly be and fit on a page. Most of my songs are in font size 18, even 20. I use Arial font, don't recommend a fancy font.