Joseph Lunn enlisted into the NSW Corps in June 1789 in England, he arrived in NSW aboard the Surprize in 1790. He first travelled to Norfolk Island aboard HM Supply in April 1791 with Captain William Hill and returned to Port Jackson aboard the Daedalus in November 1794. Joseph returned to Norfolk Island aboard HM Supply in October 1796. He returned to NSW once again and made his third voyage to Norfolk island aboard HMS Buffalo in May 1803.
Joseph returned to Sydney on 24 Feb 1805. Ships News: On Tuesday sailed His Majesty’s armed vessel Investigator for Norfolk Island, to return with a part of the Civil and Military Establishment and prisoners stationed on that Island.
Joseph Lunn, Private NSW Corps drowned at Sydney 10 Oct 1806, he was buried at the old Sydney Burial Ground.
 Sydney Gazette, 13 January 1805, p. 4.