You'll need to silence the parrot by the ship (have Critter lure him away with peanuts, then Nate can remove the lid from under his perch and cover it with the parrot's blanket ... parrot returns, falls into barrel, and you pop the lid on).
Then swap the bartender's fez for the one Nate found in a crate after the parrot was trapped. You can swap the fez by having the bartender mix a drink ... he'll remove his hat and you can make the swept. Be quick or you'll need to have him mix that drink a second time! When he puts the new fez on, it'll cover his eyes and he'll knock himself out.
Then you can grab the lamp. Cut scenes will force the proper sequence after the bartender is out of the way.