Dillon, Sir Robert (d. 1579), judge, was the third son of James Dillon of Riverstown, Co. Meath, and Elizabeth, daughter of Bartholomew Bathe of Dullardstown. He became a lawyer, probably having been trained at the inns of court in London, and was appointed attorney-general of Ireland on 9 June 1534. His path into government office was facilitated by his family connections. His father had been chief remembrancer and second baron of the exchequer, while his eldest brother, Sir Bartholomew Dillon, had risen to the post of chief justice of the king's bench in 1533. By 1537 the government was preparing to confiscate the properties of the religious houses in Ireland. Realising that their dissolution was inevitable, many monasteries began paying large fees and offering generous leases to well-placed lawyer-officials in order to secure the best compensation possible for their clergy. Dillon benefited greatly from this process. Despite being a catholic, he assisted in the dissolution of the Irish monasteries, for which in December 1537 he received a twenty-one-year lease of the demesne of St Peter's at Newtown, near Trim, Co. Meath. In July 1540, as a mark of special favour from Henry VIII, he was permitted to buy this land and Newtown became his main residence. He bought the Carmelite monastery at Athnecarne, Co. Meath, in 1546 and was granted a house in the precincts of St Patrick's cathedral in Dublin the following year.
In 1548 Dillon served as civil governor of Athlone. On 17 June 1554 he was promoted to the chief justiceship of the queen's bench and in July 1559 he became a member of the Irish privy council. Soon after, on 3 September 1559, he was made chief justice of the court of common pleas. He was knighted in 1567. Throughout his long career he remained aloof from the furious political struggles that often consumed his colleagues, preferring to amass quietly a considerable private estate. In 1569 he received a grant of the priory of St John the Baptist in the barony of Kilkenny West, Co. Westmeath. At some point in the 1560s or 1570s, the crown appointed him seneschal of Kilkenny-West; this position made him effective leader of the highly gaelicised Dillon clan of Kilkenny-West to whom he was distantly related. The government was seeking to use Dillon's family connections to peacefully advance its influence in a strategically important marchland.
Although he had previously been a diligent administrator, by 1567 old age and infirmity had rendered Dillon increasingly ineffective. From 1570 his duties as chief justice were performed by the second justice, and by 1574 blindness had left him completely inactive. Despite the repeated pleas of Dillon's colleagues, the queen did not replace him and he remained in office until his death, which occurred shortly before 5 July 1579.
Dillon married Genet, daughter of Edward Barnewall of Crickstown, with whom he had four sons and three daughters. His eldest son, Sir Lucas Dillon (qv), was chief baron of the exchequer.