The man stripped naked, jumped into the pen and began taunting the male and female big cats, The Guardian reported.
Zookeepers first turned a hose on the animals, which had instinctively attacked the intruder. They then fired a tranquilizer dart, but it missed the lions and instead struck the man, identified by local media as 20-year-old Franco Luis Ferrada, in the neck.
As Ferrada was being mauled, a zookeeper shot the lions with live rounds. They died a short time later. Ferrada was rushed to a local health clinic, where he was in critical condition.
Santiago police said he left what's believed to be a suicide note. "We are comparing it with other [writing samples]," said sub-commissioner Gerson Sepulveda.
Critics took to social media to complain about the handling of the incident, with many condemning the zoo for killing the lions.
But zoo director Alejandra Montalva defended her staff's actions, saying they'd followed the "established protocol" to deal with such circumstances.
"When a person's life is at risk, you have to sacrifice the animals," she said. "The shooter decided to save the life of the person and unfortunately we had to sacrifice two members of our family.”
A vigil was held for the dead lions, which had been residents at the zoo for more than 20 years, near their enclosure on Saturday night.
If you or someone you know needs help, please call 1-800-273-8255 for the National Suicide Prevention Lifeline. Outside of the U.S., please visit the International Association for Suicide Prevention for a database of international resources.