Lawrence Verney was the son of Lieutenant-Colonel Sir Harry Calvert Williams Verney, 4th Baronet by his wife Rachel Gwenyfyr Catherine, daughter of Victor Bruce, 9th Earl of Elgin.
His eldest brother was Sir Ralph Verney, 5th Baronet.
Another brother, Stephen Edmund Verney, was Bishop of Repton from 1977 to 1985.
Educated at Harrow School and Oriel College, Oxford, Verney was called to the bar by the Inner Temple in 1952.
In 1995, he became the first circuit judge to sit in the Criminal Division of the Court of Appeal.