Lancelot Armstrong was promoted to the position of surgeon in the Royal Navy 10th June 1807.  He served as assistant surgeon on board the Ajax at the Battle of Trafalgar.
Convict Ship Daphne
He was employed as Surgeon Superintendent on the convict ship Daphne in 1819.
The Daphne departed Cork on 28 May 1819, touched at Teneriffe and arrived in Port Jackson on 21st September 1819.
In October 1819 Lancelot Armstrong was on the Committee with James Bowman and Daniel McNamara, employed to make a survey of the General Hospital at Sydney. 
Cape of Good Hope
He was stationed at the Royal Navy Hospital at the Cape of Good Hope from 1831 to 1838. 
The 1841 Census records Lancelot Armstrong residing with his wife Jane at Gilnockie cottage, Cannonbie. They are both aged 50 and have three others residing with them.
Lancelot Armstrong died in 1848.
The United Servicemen published his obituary....Late of the Naval Hospital at the Cape of Good Hope.....Lancelot Armstrong at Gilnockie Cottage, Cannonbie on the 23rd ult, aged 63. The deceased served as assistant surgeon on board the Ajax at the Battle of Trafalgar. He was also on board one of the ships under Admiral Duckworth, when she blew up in the passage of the Dardanelles. He lost the whole of his clothes etc and saved his life by swimming.
An account of the disaster is given at Wikipedia - On 1 February 1807 Ajax, under the command of Captain Henry Blackwood, joined Admiral Sir John Duckworth's squadron at Malta to participate in the Dardanelles Operation. During the operation an accidental fire destroyed Ajax. The fire began on the evening of 14 February while Ajax was anchored off Tenedos. The fire began in the bread-room where the purser and his assistant had negligently left a light burning. As the fire burned out of control, the officers and crew were forced to take to the water. Although 380 people were rescued, 250 lost their lives that night, including many of the crewmen who had been at Trafalgar. Ajax burned through the night and then drifted on to the island of Tenedos where she blew up the following morning.