Peel off lemon rind along with white membrane. Thinly slice lemons, crosswise, disposing of seeds and ends.
Rinse and dry fish. If fillets are longer than 6 or 7 inches, cut in half. Season fillets with salt. Dredge in flour, shake off extra, and arrange on a sheet of plastic wrap.
Heat 2 tablespoons butter in a frying pan set over medium-high heat. Lay half the fish in pan and cook 1 1/2 to 2 minutes or until browned on bottom. Flip fish and cook 1 to 2 minutes. Move fish to an ovenproof platter and keep warm in a 200 degree F oven. Heat 1 tablespoon butter and cook other half of fish.
Wipe pan clean and re-heat. Melt 1 to 2 tablespoons butter and add in capers. Pour in lemon juice, take pan off of heat, and add 3 tablespoons parsley. Spoon butter mixture over fish. Top with lemon slices, the rest of the parsley, and white pepper.