Relieving Auckland City district commander Acting Superintendent Sunny Patel said about 10.56am on October 6 - a day after the brutal attack at the dairy took place - police found the Lam unresponsive in a cell.
Patel said police immediately administered first aid and called an ambulance.
Lam was then transported to Auckland City Hospital but died on October 8, police said.
“A critical incident investigation is now under way, and the Independent Police Conduct Authority [IPCA] has been notified,” Patel said.
As standard procedure, police have also notified WorkSafe of the incident at the Auckland Custody Unit.
A man and a woman were stabbed in the October 5 attack at the New Windsor Dairy and Lotto shop on New Windsor Rd.
Detective Inspector Glenn Baldwin said at the time members of the public helped arrest the man.
Dairy and Business Owners’ Group chairman Sunny Kaushal said then news of the attack was “heartbreaking”.
“We have already had deaths in our industry, and we were fearing more violence because the Government is failing to take any action. New Zealanders are sick and tired of the lawlessness.”