As McGrath says above, there were several "new" songs to the tune of "Lili Marleen." In Kiss Me Goodnight, Sergeant Major: The Songs and Ballads of World War II, by Martin Page (Panther, 1975), we find "The Dive Bombers' Song"; "My Faithless English Rose"; "The D-Day Dodgers"; "The Irish Fusiliers"; and "Going Round the Bend." They are not parodies in the strict sense of the word.