Lohan "put me through one of the most frightening experiences of my life," Tracie Rice said in a statement issued after the lawsuit was filed in Los Angeles County Superior Court.
"What Miss Lohan did that night was extremely dangerous and reprehensible. Someone could easily have been killed or seriously hurt because of her irresponsible decisions that evening," Rice said.
The suit also alleges intentional infliction of emotional distress. It seeks unspecified damages and also payment of medical and other expenses related to emotional distress.
An email to Lohan's publicist and a telephone message left for her attorney were not immediately returned.
Lohan was arrested for investigation of misdemeanor driving under the influence and with a suspended license and felony cocaine possession after last month's pre-dawn chase that ended in Santa Monica.
The suit does not provide a reason for the chase. However, two men who claim they were unwilling passengers in the car driven by Lohan have said she was upset with the daughter of Michelle Peck.
Peck was driving the vehicle carrying Rice.
Rice "was convinced that their lives were in danger and that they had to outrun the pursuing car or they might be killed," the suit said.
Peck finally drove through a barricade and into the parking lot at the Santa Monica Civic Center next to police headquarters and the SUV followed, the suit said.
Rice got out and ran toward police officers and saw a woman, who
turned out to be Lohan, run from the SUV toward her, she contended.
"Police officers approached all of them with guns drawn," the suit said.
Lohan was arrested a short time later.