Lynch was among the first of his family to become a lawyer, and several of his younger sons followed him into this profession, as did, under his influence, Patrick D'Arcy, Richard Martyn, and Geoffrey Browne as well as many of the later generations of the Tribes of Galway.
In or after 1603 Henry Lynch married Elizabeth, daughter of Richard Martyn and widow of James D'Arcy.
Henry and Elizabeth had three sons: —and three daughters: Lynch was the Galway land agent (i.e. estate manager) for Richard Burke, 4th Earl of Clanricarde, who lived in south-east England.
He was a mentor to his stepson Patrick D'Arcy and his nephew Richard Martyn, who later became senior political figures of Confederate Ireland.
Sir Henry Lynch died 21 February 1635 and was buried in the church of St Nicholas in Galway.