He was educated at Sydney Grammar School. Andrew was well liked and popular at school. Lesnie finished 6th form and his Higher School Certificate in 1974. He started his career in 1978 as an assistant camera operator on the film Patrick (1978) while he was still in school at Australian Film, Television and Radio School (AFTRS). sd

His first job after graduation in 1979 was as a cameraman on the Logie Award-winning Australian magazine-style afternoon TV show Simon Townsend's Wonder World. Simon Townsend gave Lesnie almost daily opportunities to develop his craft with little restriction over a wide variety of stories and situations, and to experiment with camera and lighting techniques in hundreds of locations and situations. After two years of working on the show, Lesnie moved on to numerous Australian film and television productions, including the mini-series Bodyline.

Later, he worked as a second camera assistant on the film The Killing of Angel Street (1981).

Lesnie would then go on to develop his craft as he photographed films such as Stations (1983), The Delinquents (1989), Temptation of the Monk (1993), and Spider and Rose (1994).

His work began receiving major attention after the release of the anthropomorphic pig story Babe (1995) and its sequel, Babe: Pig in the City. He was Director of photography on Peter Jackson's Lord of the Rings trilogy, and received an Oscar for his work on The Lord of the Rings: The Fellowship of the Ring in 2002. Since then, he filmed several other Jackson-directed films, including King Kong and The Lovely Bones, and also filmed The Hobbit films directed by Jackson.

Lesnie's final film, The Water Diviner, directed by and starring Russell Crowe, was released in Australia in December 2014 and in America in April 2015, one week before his death.

Lesnie lived on Sydney's north coast. He was a member of both the Australian Cinematographers Society and the American Society of Cinematographers. Lesnie died of a heart attack in his Sydney home on 27 April 2015.