I just won this on eBay from a German-seeming person (who lives in California). It looks different from any Laco I've seen. Here's his description on eBay:
I would like to offer for your consideration this rare vintage watch WWII Military Laco. Good working condition,keeping the right time.This rare vintage piece has an original signature on back of its case,movement.. 17 jewel signed manual wind hack setting movement, with [frosted gilt] finish, caliber 550, near mint stainless alloy signed rectangular case (39x21mm), near mint original signed dial, with luminous numerals, sub seconds. Fairly hard to find: signed Laco, made for the German market, circa 1930s!
Thank you for your help.