This rifle is quite original, meaning to its original manufacture, which is unusual because most rifles that stayed in German hands went through a number of reworks, especially those that had a long service life. This rifle was probably a black rifle, one that was hidden and pulled out late, went through an upgrade quite late, the e/135 scale is a good sign of this, but most of all it is unusual for being so factory-original (which suggests it wasn't in service in the interwar period).
Most of the parts outside of the RS are original, that is the stock, bolt, barrel are original – it is not common for a upgraded G98 to be so original. SS reworks sometimes are an exception, they do seem to re-use many original parts, but typically the Army was less sentimental about replacing parts.
The LK5 is as Ryan (I think it was Ryan) who outlined it for you, unknown, but believed to be related to the Luftgaukommando's (Luftgau Headquarters, similar to the Wehrkreis system)
Thanks for sharing the rifle and being so thorough!