Born the son of William Lambert of Banstead and Marie Bennet, Lambert was schooled at Newcastle High School before going as a scholar to Christ's College, Cambridge, where he read the Classical Tripos, graduating Bachelor of Arts (BA) in 1894 and proceeding Master of Arts (Cambridge) (MA Cantab) in 1898.
He became domestic chaplain to William Maclagan, Archbishop of York, in 1901, moving to become sub-warden of the Bishop's Hostel and Tutor of the Scholae Cancellarii, Lincoln in 1904 and holding licence to preach in that diocese.
In 1911, he became Principal of the Clergy Training School (now Westcott House, Cambridge) until 1917, when he became both Vicar of All Hallows-by-the-Tower and Warden of the Mission College of All Hallows.
He additionally became Archdeacon of Hampstead and an examining chaplain to Arthur Winnington-Ingram, Bishop of London, in 1920, both of which roles he retained when he moved from All Hallows to become Rector of St James's Piccadilly in 1922.
He was Select Preacher to the University of Cambridge in 1913, 1917, 1930 and 1941; his devotional address from the Pan-Anglican Congress, 1908 was published; he edited the Letters of Herbert Hammond Jeaffreson (1916); and wrote Life in the Spirit (1951).