Levy-Lawson was the son of Joseph Moses Levy and his wife Esther (née Cohen). His father had acquired the Daily Telegraph in 1855 only months after its founding. Levy-Lawson was editor and in control of the paper long before his father's death in 1888 and from 1885 he was managing proprietor and sole controller, becoming even more influential than his father on Fleet Street. In 1875 he assumed by Royal license the surname of Lawson in addition to and after that of Levy. Levy-Lawson was created a Baronet, of Hall Barn in the County of Buckingham, in 1892 and in 1903 he was raised to the peerage as Baron Burnham, of Hall Barn in the Parish of Beaconsfield in the County of Buckingham.
Lord Burnham married Harriette Georgiana, daughter of Benjamin Nottingham Webster, in 1862. She died in 1897. Burnham died in January 1916, aged 82, and was succeeded in the barony by his eldest son Harry, who was created Viscount Burnham in 1919.