English songs sung in Ireland become "Irish" just as Scots songs sung anywhere become known as being from wherever they are sung.
There is a huge Anglo-Irish repertoire; fifty-plus Child ballads were recovered in Ireland between the late 1960s and the mid-90s, many of them having disappeared elsewhere from the tradition, some of them a century or so before - making them 'Irish', though very few, if any originated here.
Apropos of nothing, in rural Ireland 'liss' refers to a fort or forth, an Iron age settlement believed in tradition to be the home of fairies - the "little" or "good" people.
They have been protected by superstition through the centuries, never built on or worked out of respect for their believed origins and are now widely recognised as major saviours of Irish archaeology.   
Jim Carroll