Help with Unit Markings

[mrloblolly]

I recently obtained a DWM luger with a barrel date of 1910,4 digit sn all matching,on the front gipstrap is 13.T.L.3.20. this luger is also engraved(about 70%) with ivory grips,the holster has matching # in it aswell. I would like to find out as much history and information on this piece as possible.