This song was sung by American, German, British and who knows what other troops. One particular woman made it a world wide phenomenon.
When I was at UNM in Albuquerque during the early 1970's, there was a pizza/beer joint at Bataan park, near the campus. It was popular with Navy and Marine reservists from the area, Air Force people from Kirtland AFB, and with soldiers from Sandia Army Post. This song was on the juke box, and I can remember the place being packed after drill days, with the pitchers of beer passing around and people roaring out this song through the cigarette smoke.
There were a lot of military drinking songs on that machine, but this one always stuck in my mind.
This is one of my favorite Vera Lynn songs. She had so many beautiful songs it's hard to pick favorites. "There'll Always be an England" is a good one too, but I think this is my favorite.
Kymber is completely right. Lili Marlene was Marlene Dietrich's song.