Yes, each tube experienced proof and the initials "LK" would be for a barrel finisher or fitter depending on the location of the intials(early on closer to the flats was the tube maker/barrel fella but that may have changed with time and mechanization). My 1st guess is that it probably would be one of the Kelber boys who early on invested in mechanized barrel making machines or automated barrel drawing devices. Louis Kelber of Suhl was an expert in the tube making field in the 1930s. If it is a "L", and possibly not a script "F", another possiblity is one the Klett boys, namely Louis Klett who owned Heinrich Christoph Klett & Sohne of Zella-Mehlis in the 1930s, which would mate with your 1935 proof date. But for some reason I seem to recall he as listed as a stocker during that period but being from a long line of tube makers, tube making just may have been his other area of expertise along with stocking. Thanks for the effort.