LINDSAY LOHAN was arrested early yesterday morning at a nightclub . . . (--Where else, right?) . . . for allegedly punching another woman in the face.  And it may have had something to do with a free psychic reading.

--There are about a million different versions of exactly what happened.  We'll break it down for you as simply as we can.

--It was 4:00 A.M. at a New York City club called Avenue, when Lindsay decided to punch a 28-year-old woman named Tiffany Eve Mitchell in the face. 

--Sources say they were sitting at adjacent booths, and at one point, Lindsay told the woman to, quote, "give me my space."  Shortly after that, she punched her.

--Police were called, and by the time they got there, Lindsay had already tried to flee.

--She was in the passenger seat of a car outside the bar, but cops intercepted her and arrested her right there.  She was booked for 3rd degree misdemeanor assault and released at around 8:00 A.M.

(--TMZ has videos of Lindsay's arrest and release.  In the arrest video, you can hear her saying, "Are you kidding me?"  And in the release video, she's covering her head with a coat to shield herself from the paparazzi.)