Born in
Exeter on 10 November 1641, Lake was the son of a clergyman, and his early life seems to have been connected with the
Earl of Bath's family. In 1658 he entered
Wadham College, Oxford, as a commoner, and was elected a scholar in 1659. About 1670, Lake became chaplain and tutor to the princesses
Mary and
Anne, the daughters of
James, Duke of York. He was made prebendary of
Exeter Cathedral on 13 December 1675, and archdeacon of Exeter on 24 Oct. 1676. In 1676 he was created D.D. at Cambridge by royal mandate. On 5 January 1681,, he was elected a brother of
St. Katharine's Hospital, of which he was also a commissary, resigning in 1698. On 30 November 1682 he was instituted to the rectory of
St. Mary-at-Hill, to which was annexed in 1700 that of
St. Andrew Hubbard. Lake was an admired preacher. He died on 1 February 1704, and was buried in
St. Katharine, Tower Hill, where there was an inscribed monument. ==Works==