By placing advertisements on their site, Rap Genius could generate significant revenue, with Web traffic that would make almost any content-driven site green with envy. Lots of other avenues are open for turning the site into a business. A premium version of the site is one possibility. Creating sponsored pages, where musicians or labels generate activity around new album releases and other content. There have been discussions with an agent to pitch network Comedy Central the idea of a Rap Genius television show, which could be similar to Mystery Science Theater 3000.
So no monetization strategy has (had?) actually been deployed yet.
edit: they ask for it