The Irish element in Long Day's Journey into Night is present from the very start. The family depicted in the play are called Tyrone, a very Irish name, which also happens to be one of the nine counties of Ulster. Mary Cavan Tyrone, the morphine-addled family matriarch, has a distinctly Irish middle name, which, like her surname, is the name of an Irish county.
The patriarch of the family, the actor James Tyrone, was born in Ireland and emigrated to the United States with his family at the age of nine. He's fiercely proud of his ancestry and often alludes to it, though not always in a particularly flattering way, such as when he admits that he gave whiskey to his sons as medicine when they were little. The implication is that this is part of some old Irish tradition. (The word "whiskey" literally means "water of life," so it's not too difficult to see where this tradition might have come from).
James also refers to his father's deserting his family and returning to Ireland, where he committed suicide. However James Tyrone Sr. might try to romanticize his background, less savory glimpses of his troubled past such as this reveal a darker, more disturbing truth about his Irish ancestry.