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.
How would the addition of reviews exempt a lyrics site from copyright law?
The music industry doesn't go after these sites because it's like playing that whack the mole game.
They played "whack-a-mole" with illegal music downloads, and went after file sharing services with a vengeance. Much more likely, they are presently choosing not to go after lyrics sites because they help the sales of music and merchandise, and there's not much of a market for their separate sale.