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He was the second but eldest surviving son of Charles Lambart, 3rd Earl of Cavan, and Castilina Gilbert. He inherited the Earldom of Cavan in 1702, his eldest brother Charles having predeceased their father.
He married Margaret Trant, daughter of Richard Trant, Governor of Barbados, and had four children, including Ford Lambart, 5th Earl of Cavan, and Gertrude who married William Fitzmaurice, 2nd Earl of Kerry.