Fan sites are fine if they write and get explicit permission to use the lyrics or they review the lyrics as opposed to just displaying them.
The music industry doesn't go after these sites because it's like playing that whack the mole game. However, I wonder how much culpability Google merits. It seems that they cover their behinds by banning these kinds of sites in their TOS. Yet, since they don't enforce that document, they are in fact partnering up with these sites. The danger for Google, I think, is that they are a big enough target to go after.