Thomas Smith was born in England around 1707, the illegitimate son of Sir Thomas Lyttelton, 4th Baronet, and an unknown woman. Raised as a member of the Lyttleton family, he joined the Royal Navy and became a junior lieutenant on the Royal Oak in 1727. In 1729, while a first lieutenant on the Gosport , he created controversy when, acting as commanding officer in the absence of the ship's captain, he compelled a French corvette in Plymouth Sound to lower its topsails in salute. This insult to France nearly ended his career; Smith was immediately court-martialed and dismissed from service, but was reinstated the next day after a popular outcry.
In 1730, Smith was promoted to captain of the 24-gun Success , and two years later, received command of the Dursley in the Mediterranean. His primary duty was to patrol for Barbary pirates, a position that he held for eight years. He then served two single-year terms as governor of Newfoundland in 1741 and 1743, during which time he also commanded the Romney , and was ordered to protect Newfoundland's fisheries. In 1746, received a promotion to rear-admiral, and was commander-in-chief at the Downs in 1755. In that capacity, he presided at the trial of Admiral John Byng, which resulted in Byng's execution. Smith became a full admiral in 1757. He died in 1762.