The oak stand is not original. It is one I made a while ago. Also I don't think the vitreosil globe is right for its age. What I find interesting about this is the date stamp on the side. VERY difficult to see if you are not looking for it. If you have a painted KL, have a real close look. You may have one too.
It's a fine lamp! When that tank was fitted in an Oak stand Tilley called it an ML., 98. https://classicpressurelamps.com/attachments/1294960010-1939-06-jpg.17165/