He was the son of Ralph and Frances Partridge, and named after Lytton Strachey. In 1962, Burgo married Henrietta Garnett, daughter of Angelica Garnett and David Garnett. At the wedding, seventeen-year-old Henrietta was already pregnant with their daughter. Burgo died suddenly of heart failure on 7 September 1963, only three weeks after the birth of their baby, Sophie Vanessa. He had already been noticed for his writing ability, and had published one well-received book, A History of Orgies (1958), which was a financial success for himself and his publisher Anthony Blond.