Born in Pield Heath, raised in Bournemouth, and educated at Queens' College, Cambridge (1912–1915), Lambert served as a platoon commander in the Gloucestershire Regiment during World War I, and was wounded at the Battle of the Somme in July 1916.
After his demobilization in 1919, Lambert remained in East Africa and was appointed assistant District Commissioner on the southern coast of Kenya.
His subsequent postings were as District Commissioner in Kiambu, Lamu, Embu, Kenya, Voi, and other places, where he gained an "outstanding" reputation as an administrator known for his "profound" knowledge of indigenous law and culture (especially Kikuyu).
Controversially, Lambert advocated early initiation for young women in Meru District, involving female genital mutilation (FGM).
When Lambert left Meru in 1937, he informed his successor that "propaganda" encouraging early initiation had been entirely successful".