In early 2001, Purdue Pharma LP executives discussed how to respond to abuse of the company’s five-year-old prescription painkiller OxyContin.

Richard Sackler, an owner of the powerful opioid’s maker, saw two clear groups of OxyContin users: legitimate patients and reckless criminals, according to a newly amended lawsuit filed by New York Attorney General Letitia James. He objected in an internal company email to “criminal addicts…being glorified as some sort of populist victim,” the lawsuit says.

In...