Kelly died Wednesday night in her sleep, according to her agent, Craig Wyckoff.
"Lisa had voluntarily checked herself into a treatment facility early this week where she was battling the addiction problems that have plagued her these past few years," Wyckoff said in a statement.
He said when he spoke to her Monday, she was "hopeful and confident, looking forward to putting this part of her life behind her."
"Last night she lost the battle," he said.
The cause of death has not yet been determined.
Kelly had a string of run-ins with the law in recent years. She was arrested in Burbank in June on suspicion of drunk driving, and she was arrested twice in 2012 for alleged spousal assault.
Kelly played Laurie Forman, sister of Topher Grace's lead character Eric, on the FOX series, which ended in 2006.