The animal escaped from an area that was supposed to have been locked, and attacked 22-year-old Alexandra Black.
She'd only worked at the Conservators Center in North Carolina for about two weeks.
In a statement, her family described her as a "beautiful young woman who had just started her career."
They continued: "There was a terrible accident, and we are mourning. But, she died following her passion."
Tranquilising the lion failed as attempts were made to retrieve the young womans body.
Police said that it was then shot and killed.
Mindy Stinner, the executive director of the Conservators Center, told WTVD-TV: "This is the worst day of my life.
"We've lost a person, we've lost an animal.
"We have lost the faith in ourselves a little today."