On wikisource.org ("The Free Library") lots of texts (and other documents) are published, including song lyrics.
As an example there are currently 163 pages in the "Song lyrics" category in the English-speaking section: http://en.wikisource.org/wiki/Category:Song_lyrics

All of these are free to share. The copyright policy is at http://en.wikisource.org/wiki/Wikisource:Copyright_policy .
(In most cases it's works in the public domain.)

My suggestion is to add the whole of wikisource.org as an allowed lyrics site. They have different subdomains for different languages, like en.wikisource.org for English. All in all there seems to be 184 languages represented currently, and it seems better to handle this as one site than a lots of sites.