Taking holy orders, he was successively a minor canon of Durham Cathedral, perpetual curate of South Shields, and from 1747 vicar of Norham in Northumberland, where he remained for the rest of his life.
Suddenly determining to marry Philadelphia Nelson, the daughter of a Durham carrier, whom he had seen only once, and that many years before, he sent a proposal to her by letter, inviting her to meet him on Berwick pier, and bidding her carry a tea-caddy under her arm for purposes of identification.
His chief work, however, was An Exact and Circumstantial History of the Battle of Flodden, in verse, written about the time of Queen Elizabeth (1774, 1809).
This is said to be published from a manuscript in the possession of John Askew of Pallingsburn, Northumberland; the notes, especially those on etymology, are numerous and very curious.
Lambe was also the author of the ballad "The Laidly Worm of Spindleston Heugh", which William Hutchinson thought ancient, and inserted in his history of Northumberland.