How do I fix stiff dual-pivot brakes?
This is a rear case that I would use WD40 or even engine degreaser on a bike part. Remove the pads, drown the brake in one of these and work it till its free. Might be worth removing from bike and soaking in a bath. 

I would no dismatle it unless the above did not work. 

Once the part is moving freely it will have no lube on it. Clean it with hot soapy water, dry it out and use a dry lube rather than a wet lube -  it won't attract the dirt. Alternately use a wet lube but regularly re lube it.