AirPrint on a HP MFD?

I'm trying to get an iPhone to see a HP MFP via AirPrint.

The printer has wireless installed and can accept a print from an Android phone, it can also accept a print from said Android device via WiFi-Direct.

What do you have to configure, all I can find is a bunch of priority settings that I don't quite understand, like lpd auto & lpd raw.

Anybody have any clue why our E77830 doesn't show up on an iDevice?