There's a song Caitlín Ní Uallacháin by Liam Ó hIfearnáin/William Heffernan (Liam Dall, lived circa 1720-1803). Jill Rogoff sent me a copy. she says the tune is called "Kathleen Nowlan"; that is another anglised form of the name besides Houlihan. You can also find the song is Petrie's "Ancient Music of Ireland", complete with notes and translation.