Allen,
What have you searched regarding Luxembourg? Could he have come from the city of Luxembourg and perhaps been an ethnic German living there? Also there could have been German occupation in the country of Luxembourg during your ancestor's time.
It seems your ancestor was German speaking and probably an ethnic German given what they state on his death certificate. On my mother's maternal line her ancestors came from Northern Bohemia but they spoke German and listed that they were German coming from Germany. In my research I found that the family line was in Northern Bohemia as long ago as 1500 but still called themselves German coming from Germany. Granted they were near the border etc.
Best wishes, Pam