I would also like to know if electrolysis has been successfully used on shotgun barrels. I have given it much thought but have never got around to trying it.
I have used electrolysis on everything from trigger guards to car doors and it certainly has advantages compared to other methods.
One major advantage is that there is no abrasion so no fine details on the surface are lost.
The major disadvantage of electrolysis is it only works on line of sight. The surface you are cleaning has to be at least partially facing the anode. On a car door, etc., one has to fit anodes inside the cavity.
On the bore of a barrel this would involve the anode running through the length of the barrel without making contact with the barrels. A piece of quarter inch rod with some small pieces of rubber( short sections of 1/4" rubber fuel line, maybe?) to prevent contact with the barrels would probably do the trick.
Lye is far more aggressive than washing soda or TSP and always my electrolyte of choice. It is not suitable for painted surfaces but that is obviously not an issue for firearms.
Electrolysis is NOT suitable for case colors. It doesn't completely remove the color but it dulls them.