Lindsay Lohan -- I'm Hiring a Private Investigator

Lindsay Lohan is not just going to sit around and wait for Tiffany Mitchell to sue her ... so she's hired a private investigator to dig in to the life of the woman who accused LiLo of assault ... TMZ has learned.

As TMZ previously reported, Mitchell has hired the omnipotent Gloria Allred to represent her following an alleged altercation with Lindsay in a New York nightclub.

But sources close to Lindsay tell TMZ the "Liz & Dick" star feels Mitchell just made up the story about Lindsay punching her to score a quick payday.

We're told Lindsay feels Mitchell is just another in a long line of people who see Lindsay as an opportunity to make a buck off her ... and the fact that Mitchell hired Allred of all people just proves that.

According to our sources, Lindsay has hired a P.I. to look into Mitchell and see if she has any criminal past or if she's done anything like this before. We're told Lindsay wants to dig up as much info on Mitchell as she can so she's ready should Mitchell pursue the case in civil court.