Electrolytic rust removal is is fairly safe, not much can go wrong. However, you may not get out much of the rust inside of threaded areas. If an area is "shielded" the electrical current won't want to flow from the shielded area and the rust won't want to leave that area.

Still, it would not hurt to give it a shot.

Warm oil might do more than cold oil. If you can figure out a safe way to warm up a PB Blaster filled container (hot plate maybe?)with the lantern in it you should get better penetration into the rust.

Just to give you something to compare to, I removed a burner cover from a dietz torch this summer, trying methods starting very gentle and finally suceceding with an "all or nothing" pipe wrench and a 4# hammer. I'm not saying to try a 4# hammer with the glass font in there, but that some amount of rotationally applied "tapping" may succeed where mere twisting with all your might doesn't work. Heck if I know how to do that without damaging something, but frustration often causes creative ideas to happen.

Good luck and let me know if you get it off.

Rick