What the Remington factory used to recommend for parkerized shotguns was to field strip the gun per the owner's manual, including the magazine.
Lay the gun on a thick pad of newspaper and spray the entire gun, inside and out with a dripping wet coat of Rem-Oil or CLP Breakfree.
Allow to soak for 30 minutes to dissolve the old lube and dirt and "soak in" the new.
Wipe dry and reassemble.
This will lubricate the gun and impregnate the rough parkerized coating with a protective coat of lube.
Every time you use or handle the gun, apply a little more lube with a tooth brush or lint-free small cloth to keep the protective coating.
DON'T soak the stock or forearm, just the metal, inside and out.
I prefer CLP Breakfree, because its a little thicker than the Rem-Oil, and it builds up a protective layer of Teflon in-on the metal.
One reason parkerizing is a good finish, is because the rough surface holds lube so well and forms a protective barrier to rust.