I did a bit of research, the largest website for lyrics is metrolyrics.com, they are owned by CBS (as of October 2011) and they license all their lyrics through a company called Gracenote (http://en.wikipedia.org/wiki/Gracenote) it's plausible that Rapgenius are also licensing through this company, or similar? Seems there is a way for a lyric website to exist legitimately.

The, ahem, "genius" of Rap Genius is that the commentary aspect goes a long way towards establishing fair use for the lyrics.

I think when a service is so obviously beneficial to the artist, like Rap Genius, the industry will find a way to work with them as opposed to suing them. This only helps theor bottom line.