Push notifications are still the domain of text messages and native applications, and as such Tran is waiting for the W3C and other standards bodies to incorporate the relevant API (application programming interface) for web technologies.
For Rap Genius, doing the same for the internet will mean pulling in large swaths of text from outside the music world, as the site has already started to do, hosting annotated versions of public domain books like The Great Gatsby and court cases like Plessy v.