There would have been Irish men in Liverpool working on both the docks and on the ships. Irish sailors or dockers or labourers could have taken it back to Ireland. Limerick is a port like Liverpool so the song could easily go either way.

My feeling is that the Liverpool song came first because I can't imagine a more polite song such as "Limerick" being taken up and reworked by dockers and sailors in Liverpool. I can imagine the chorus and melody of "Liverpool" being admired and reworked for Irish folk music.

The words of "Limerick" are in observer mode rather than first person like "Liverpool". Maybe the writer of the Limerick song is revealing his distance from the song's origins. We'll probably never get to the bottom of this mystery.

MV