Comhghairdeas a Mhairtín!

I'm thinking that the word 'Titharally' in this song is an anglicized spelling/pronunciation of the word(s) 'tíargálaí', 'tíaralaí' or 'tíarnúilí', all of which could be used to mean 'Lords' or 'Dominions'. Each of these words have their root in the word 'tír', which means 'land', 'country', 'state', 'nation'.

Hoping this helps, Áine