Sorry goldfish! I somehow missed your post.
I will try to keep it short! It is a consequence of WWII, more precisely the "Battle of the Bulge". After the battle was over there were tens of thousands of small arms and UXOs covering the countryside and villages. There was no one there to pick them up. The army was started from zilch and police had suffered losses during the war. Very soon the kids started picking up all the "toys" and fooling around. There were many wounded and quite a few dead, as well from gunshot wounds as from exploding ordnance. So the adults started sanitising the countryside. They put all the UXOs either in disused wells or in the mill channels. Most small arms were just put away, hidden somewhere in the barn or the house. So traditionally gun laws in Luxembourg were very liberal. If you found an old gun form WWII in your house it was very easy to register and thus legalise it. The government was happy to know where the guns were and preferred to have a nearly complete register, then to have thousands of illegal guns, nobody knew about, floating around.