Rafflesbear had a couple of questions:

I am getting visions of the American mid-west here - the lack of water does not suggest the UK
and
are the names Liza and Henry more popular in one region than another and do they give a clue to the ethnicity of the subjects?

I've always (mis?)understood or felt this song to be from the
southern Appalachian mountains. Mainly this is because of the names of the characters, Liza and Henry. Liza is a short or pet version
of Elizabeth, with great historical and cultural connections to England, and Henry is, likewise.

The southern Appalachians were mainly settled from England. While I haven't done or even read of a name census of the US, I expect that
one would find Elizabeth or Liza and Henry disproportionately
represented there. Hardly conclusive evidence, of course, but
that's my impression, and I'm sticking with it.

Dave Oesterreich