Lohan wrote in a sworn declaration that she is frightened of the 38-year-old man.
Text messages attached to Lohan's petition state the sender believes he and Lohan are engaged, and has left her a box of chocolates and other items.
He claimed in one message that he was in the courtroom last month when the 24-year-old actress was sentenced to 120 days in jail.
Lohan's publicist, Steve Honig, said he would not comment on Lohan's security matters.
