You can find a function here which I believe does what you want:
http://www.mail-archive.com/lilypond-user%40gnu.org/msg81870.html
It's been a while, but it looks like you add \tagIt at the line beginning,
to any of the verses, This will center the lines based on the longest word
and left-justify, regardless of the verse to which you attach the \tagIt.
Attached is the relevant code with your example.
Of course it would be great to automate this so you wouldn't have to worry
about line breaks, and possibly that could be done here.
Hope this helps,
David
P.S. I see the following message in the above thread:
http://www.mail-archive.com/lilypond-user%40gnu.org/msg81941.html
Possibly you could request the code from the poster.