Balfour was born in
Bonnington, Edinburgh, on 9 March 1854 the son of James Balfour Melville (1815–1898) and his wife, Eliza Ogilvy Heriot Maitland (1821–1887). He was educated at the
Edinburgh Academy and the
University of Edinburgh, he became a
lawyer by profession, rising to be a
Writer to the Signet. In 1893 the family changed its name to Balfour-Melville when his father succeeded to the estate of
Mount Melville near
St Andrews,
Fife. His Edinburgh residence was at 53 Hanover Street in
Edinburgh's New Town. His son
James also played cricket for Scotland before losing his life in the
First World War. Balfour-Melville died in
North Berwick,
East Lothian, on 16 July 1937. He is buried with his parents in the family tomb in the south-west corner of
Greyfriars Kirkyard close to the Robertson mausoleum. On his grave he is named simply as
Leslie Melville. ==Cricket career==