Alan Lomax was not always the most careful transcriber of lyrics.
Just compare "The Foggy, Foggy Dew" in Folksongs of North America with his stated source, Sandburg's American Songbag. Lomax's printing of "Frankie and Johnny" in the same book elicited a published rebuke from its original collector; for one thing, the collected text had "Albert" as the cheatin' man!

There's no need to assume that the 1964 "British Sergeant" represents an independent traditional text.