It's a drum type brake and apparently has a small hydraulic reservoir as part of it. It uses ATF. The ATF seems to be an oil bath for the bearings inside. The driveshaft spins whenever the tranny is in gear, so the bearings are in pretty much constant motion.
I found this techref online but it's for a 2008. It doesn't say much about lubing, though.
http://www.justanswer.com/uploads/molurch/2008-03-12_095729_brake.pdf
It's true that it's "not like a car", which typically has an actual pin that slides in and locks the wheels when in Park. That mechanism isn't strong enough for heavy vehicles, so they use an "auto-park brake", basically just a brake that is automatically applied when the transmission is put into park or the emergency/park brake is set. But that's a technical difference and not one the driver is supposed to worry about. Just use transmission Park and/or the Park/emergency brake as you would in any vehicle.