Yes, that stanza has the offhand feel of something extemporized on a stage, and seems not to fit easily in the tradition otherwise.

As for "Lu," that was my best guess at what I heard Galvin singing. It would stand for Louise I suppose.

Actually, "Liza" though uncommon in Britain is not all that rare in the US (perhaps due to the longtime popularity of Liza Minelli), might be more common these days as a nickname for Elizabeth than "Betty." And I know a Mary Louise who prefers to be called "Lou." Not to mention the "Lady whose name was Lou" in song & story, exact reference not recalled.