as Martin says, you'll get two versions in the DT under Shule Aroon, also one under the title "Buttermilk Hill". I think Buttermilk Hill comes from the American Civil War and the progenitor from late 17th century (the Irish language version mentions the defeat of King James and the flight of the 'wild geese'to mainland Europe- related to the English language lyrics in early versions of the song: 'Now my love has gone to France') Irish spelling of Shule Aroon, phoneticised in the DT:

Siúl,Siúl,Siúl, a rúin
Siúl go socair agus siúl go ciúin
Siúl go* doras
Agus ealaigh liom
Is go dté tú mo mhúirnín slán

[*or 'go dtí an' or 'dhan'-take your choice/ DT database gives 'dheen' - closest to 'go dtí an']

An Irish language version with the same basic story and a similar air goes (as well as I can remember it):

chorus: Siúl,Siúl,Siúl a ghrá
Níl leigheas ar fáil ach leigheas an bháis
Ó d'fhag tú mise is bocht mo chás
Is go dté tú mo mhúirnín slán

A bhuachaillín aobhínn alainn ó
Is lán do chroí 'us is deas do phóg
Ma fagfaidh tú mise, ní bheidh mé beo [?]
Is go dté tú mo mhúirnín slán

Is minic a bhréag tú mé ar do ghlúin
Ag cur do scéal dom féin in iúl
Ach d'fhag tú mise, is tú mo rún
Is go dté tú mo mhúirnín slán

Ach, chuireadh ar Rí Shéamais ruaig
Is d'imigh na géanna leis ar luais
D'imigh mo stóirín, 'sé cúis mo bhróin
Ó go dté tú mo mhúirnín slán