Lesnie was believed to have suffered a heart attack on Monday.
A spokesman from the Australian Cinematographers Society confirmed the news of his demise, said The Hollywood Reporter.
"We have been advised of the sudden death of Andrew," the spokesman said, adding that his family would provide an official statement later.
Lesnie spent more than a decade collaborating with director Peter Jackson on the six "Lord of the Rings" and "Hobbit" films.
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Known for balancing technology with artistic considerations, Lesnie also shot the 2011 film "Rise of the Planet of the Apes", directed by Rupert Wyatt.
The cinematographer recently polished off "The Water Diviner", the directorial debut of Russell Crowe. That movie opened Friday in US theatres.
"Devastating news from home. The master of the light, genius Andrew Lesnie has passed on," Crowe tweeted.
Lesnie won his Oscar for his work on "The Lord of the Rings: The Fellowship of the Ring". The famous trilogy was based on the novel "The Lord of the Rings" by JRR Tolkien.
Lesnie's impressive body of work also includes the post-apocalyptic science fiction film "I Am Legend" (2007), directed by Francis Lawrence and starring Will Smith; "The Last Airbender" (2010) and "Healing" (2014), helmed by Craig Monahan.
He was inducted into the Australian Cinematographers Society Hall of Fame in 2002.
Lesnie studied film and television at TAFE and at the Australian Film, Television and Radio School before joining the Australian Broadcasting Corp as a camera assistant.
He honed his craft on low-budget short films and music videos and assisted on documentaries, features and commercials. He then spent several months on Wonder World, a children's afternoon magazine-style show.