lyrics are copyright, and the owners make money by licencing that content. If you search for song lyrics on google you get official licenced ones, not crowdsourced lyrics. to give them to Genius for free would de-value their licencing deals.

if Genius was actually creating more value than the licencing deals, then i'm sure the labels would have been happy to work something out. But what's the value for the content owners to have their lyrics on Genius?