Lohan crashed into the rear of the man's 18-wheeler truck on Friday (June 8), totalling her rented Porsche.
The man, who has only given his name as James, told TMZ that after the collision the Mean Girls actress attempted to flee the scene.
James claimed he wanted to exchange info with Lohan, whom he did not recognise. When he tried to stop her, a representative from Lohan's upcoming movie Liz & Dick, who had been trailing behind the actress, picked up a pink bag, "filled it up with something" and then put clothes on top of it.
He said that the driver of the Escalade then offered to "go to the bank" and withdraw money in exchange for silence.
"Him and the [assistant] took me across the street and told me this was some kind of famous person and they didn't want to be in the media," James explains, "But I'd already called 911 because they were trying to get away from the scene. But they packed a bag and then the limousine driver told me, 'Don't mention the bag to the cops'."
Lohan returned to the set of Liz & Dick after a brief trip to the hospital.
She has yet to publicly comment on the incident.