This job is best done by removing the flintwheel - 30sec job with a jewelers screwdriver, or if it's tight a suitable screwdriver with a notch filed out of the middle.
I've seen lots where the owner has tried to force the key when the lamp is in this condition.
If you're lucky (rare) the solder attaching the crown wheel to the pinion fails & the crown wheel unscrews. Usually though, the bottom of the pinion shears, requiring the pinion to be replaced.
Takes about 1/2 hr from stripping to reassembling & testing the lamp - but you do need a 60W ish soldering iron to re-fix the crownwheel.
We inhabit an island made of coal, surrounded by a sea full of fish. How can we go wrong.......