Robert was born in Ireland, the eldest son of James Dillon and his wife Eleanor Barnewall.
His family was Old English and descended from Sir Henry Dillon who came to Ireland with Prince John in 1185.
Robert's mother, who was also called Helen instead of Eleanor,[4] was a daughter of Christopher Barnewall of Turvey House, County Dublin.
Robert and Margaret had three sons: About 1610, Dillon married secondly Dorothy, a Protestant, the fourth daughter of George Hastings, 4th Earl of Huntingdon, an English noble, widow of Sir James Stewart (died 1609), who was a son of Walter Stewart, 1st Lord Blantyre, a Scottish noble.
[11][12][13] Robert and Dorothy had a son: Dillon had been studying law in London at Gray's Inn and was called to the bar in 1613.
Dillon as well as his son James conformed to the established religion some time before his father's ennoblement.
[17][18] On 24 January 1620 Dillon's father was raised to the peerage with the title "Baron Dillon of Kilkenny-West", in the Peerage of Ireland[19] in a ceremony performed by the Lord Deputy Oliver St. John in the presence chamber of Dublin Castle on 25 January.