I think we can rule it out as a traditional song. There is no song in either the Roud Index or the Traditional Ballad Index with that first line. Neither is there a song "The Crofter's Lament." Ord has a song he calls "The Exiled Crofter's Lament," but it doesn't have that line (and isn't humorous).

Not much help, I realize, but it might save people some time looking.