Trying to help to put this topic back on its tracks.
It is a mismatching Luger, as said above. Numbering is in military style, there are remains of military acceptance proofs on the right side of the receiver and there is the notch for the Artillery rear sight over the receiver.
My bet is that this guns started its life as an Artillery Luger (LP.08) during WWI and was rebarreled with the more conventional 4 inches (100mm) barrel afer the war. Probably it was at this time that the toggle was changed in order to have the correct rear sights (fixed) for its new barrel. It was most likely aimed for civilian market after WWI.
Anyway, it would display nicely in a shadow box of your father's belonging and awards.
Thanks for sharing,
Douglas
PS - Just now I saw that Karl had provided you with much more info. Sorry for being redundant. I promisse to read the 2nd page next time!