On 13 November 1860, Lawson married Mary, daughter of Joseph Pocklington Senhouse of Netherhall, Maryport, Cumberland. Their union produced eight children; four boys, Wilfrid, Mordaunt, Arthur and Godfrey; and four girls. Ellen, Mabel, Lucy and Josephine. Ellen married Arthur Henry Holland-Hibbert, 3rd Viscount Knutsford (1855–1935), they produced one daughter named Elsie and one son named Thurstan. In 1895, Mabel married Alan de Lancey Curwen of Workington Hall, they had three children. In 1896, Lucy married Edward Heathcote Thruston of Pennal Tower, Mochgullith, North Wales In 1909 Josephine married Frederick William Chance, the member of Parliament for the city of Carlisle.