Gee Bruce, a search of the DT for "Go, Lassie, Go" brings this up:

GO, LASSIE, GO
(Stephen L. Suffet)

I walked my dear old collie,
Across the blooming bower,
But she never stopped to piddle,
Though I walked her half an hour!
Will you go, Lassie, go?

I don't recall hearing it, you must have sang it while I was seeing a man about a horse.