I'm just guessing here, but "Will you bring me to Tipperary and lay me down easy" and similar phrases in Irish Traveller versions seem to be based on "Will you carry me to the prairie" as it often appears in the "Streets of Laredo" versions.

Jim, do you remember hearing any cowboy songs from Travellers?
I remember reading somewhere that cowboy songs where quite popular with Travellers.

It looks like the cowboy song "Streets of Laredo" has influenced the earlier "Soldier Cut Down" versions in Traveller repertoires.