Could you confirm what Karl gives as his place of birth on the records you have found?
Luhmannsdorf is in the north-east corner of modern Germany; it is within one day's walk of the sea and a few days walk from the large port of Stettin (now Scczecin, Poland). Memel (now Klaipeda, Lithuania) is a major seaport over 100 miles further east. It is highly possible that Karl (Gustav) ran away to sea, signed up as a merchant seaman on various vessels before deciding that spending months at a time on board ship under tough discipline was not the life he wanted.
My gut feeling is that Luhmannsdorf is the more likely birthplace. It would not have been particularly well-known outside the local area, so Karl would probably not have heard of it if he had not been from the area.
Philip