The tune "Kitty Tyrrell" was published by the Gows in Scotland - I don't know of Scottish words for it, and as far as I know it was always seen as an Irish tune.

Except that the volume where the Gows published it also includes "Niel Gow's Lament for his Second Wife", which is a variant of the same tune. And there's no comment at all on the connection. Some kind of statement was being made there but I can't figure it out at all.

Another set of words for it is "The lambs on the green hills", which is also Irish.