Regarding the tax... YES your Luger will be subject to the National Firearms Act of 1934 IF AND ONLY IF you purchase a stock like the one you posted...and ATTACH IT to your Luger. Possession of both this stock and your Luger without registration under the NFA is NOT recommended... It could be considered "constructive intent" by the ATF.
It is NOT historically accurate for your gun because it is not the type that was issued with it... and it is NOT approved by the ATF as an exception to the Curio & Relic List that is on their website...
Let me be really clear on this before you make a serious mistake...you are subject to the tax whether you shoot it or not... The POSSESSION of such a stock ATTACHED to a pistol like yours that is NOT REGISTERED as a SHORT BARRELED RIFLE under the NFA is a federal felony.
Possession of an original or reproduction Artillery Luger stock (the flat type) that is ATTACHED to a pistol like yours is NOT subject to the provisions of the NFA, and therefore not a federal crime.
You can find much history about your model gun in a summary about the Artillery Luger on this web site:
http://lugerlp08.free.fr/
The book shown on that website was authored by the Moderator of the Artillery Luger Forum...Mauro Baudino.
The summary on his site is in English, but the book is written in Italian... the excellent photographs are also captioned in Enlish. It is the only book published that I know of that deals exclusively with the LP-08 or Lange Pistole 08...Artillery Luger.
I strongly suggest you visit the ATF website to learn more about shoulder stocks and pistols, Curios & Relics, and the National Firearms Act of 1934... because ignorance of the law would be no excuse for a felony violation for illegal possession of a short barreled rifle (SBR).
http://www.atf.treas.gov
http://www.atf.treas.gov/firearms/nfa/index.htm
http://www.atf.treas.gov/firearms/curios/intro.htm