Lam was taken to Mackay Memorial Hospital in Taipei on Tuesday and later fell into a coma, reported the South China Morning Post citing local media. He died late on Thursday.
In a post on Facebook, Taiwan President Lai Ching-te wrote that he was "deeply saddened" about Lam's death, sending condolences to his family and friends.
Lam's life "bore witness to the value of freedom of expression, and to the fear and suffering inflicted by authoritarian repression.
"He chose not to remain silent. Instead, he reopened Causeway Bay Books in Taiwan, turning it into a place where friends from Hong Kong could gather, speak out and support one another," Taiwan's leader added.
Last year, Lam told BBC Witness History: "Everyone has their own values. You can't go against your values, nor can you betray others.
"If you believe something is right, you should continue to stick to it. It's not like you're harming anyone. If everyone could do that, this would of course be a better place," Lam said, in what was his last BBC interview.
In 2015, he was arrested during a visit to mainland China and held for more than 400 days.
He was among several bookshop owners and staff who disappeared and were later found to have been detained by Chinese authorities, as part of a crackdown on bookshops in the former British colony that sold publications critical of China's leaders.
A confession broadcast on Chinese television was, he said, staged and acted out to a script.
His case fuelled fears of China's increasing encroachment on Hong Kong's freedoms, fears which led to the months-long mass protests in 2019 in Hong Kong - China's special administrative region since 1997.
