I have Dexter axles (though not ez lube) but I do have the Dexter manual, so I looked up how to pack them. According to the manual, you remove the rubber plug, place a MANUAL grease gun onto the grease fitting, and while rotating the drum, pump grease into the fitting. The old grease will start to come out around the grease gun nozzle. Keep adding grease until CLEAN grease is observed coming out. When clean grease comes out, remove the grease gun, wipe off excess grease and replace the rubber plug.
This process is similar to using a bearing packing tool, but you don't have to remove the bearings from the trailer.
I would go to the Dexter web site to see what grease they recommend. There's a complete list in the manual, but I'm not going to enter it all here.
According to the Dexter manual, "if hubs are removed from an axle with the ez lube feature, it is imperative that the seals be replaced BEFORE lubrication".
This has nothing to do with having brakes or not, just removing the hub. So, if you have ez lube bearings, I wouldn't remove the hubs unless you suspect something is wrong. Just "repack" them using the method described in the manual.
Dexter recommends doing this service every 12 months or 12,000 miles
I have Dexter EZ Lube axles and the Dexter manual that came with my trailer recommends a cleaning and repack every year. So what is any benefit of the EZ Lube system? Most folks don't travel
enough miles a year to need to add grease more than every 12 months.