Lindsay Lohan -- ARRESTED FOR FIGHTING

Lindsay Lohan was ARRESTED at 4 AM Thursday in New York City for allegedly punching a woman at a New York City nightclub ... law enforcement sources tell TMZ.

Our sources say Lohan was at Club Avenue when she got into some sort of argument with a female patron and it became physical. We're told cops came and arrested Lindsay for allegedly assaulting her.

Law enforcement tells us prior to the fight words were exchanged between Lindsay and the woman as they sat in separate booths near each other. Lindsay said something to the effect of, "Give me my space." Some time passed and then, for some reason, Lindsay allegedly punched the girl in the left side of her face.

We're told by the time cops arrived Lindsay had left the club and was a passenger in a car that was leaving the area. Cops intercepted the car and made the arrest.

While Lohan was in cuffs, she kept repeating, "Are you kidding me? Are you kidding me?"

Lindsay was booked for 3rd degree misdemeanor assault, given a desk appearance ticket (meaning she must show up in court in the near future) and released several hours after she was taken into custody. Law enforcement says she was "visibly tired" at the station.

We're told investigators went back to the club looking for security footage of the alleged altercation.

And this isn't Lindsay's only legal problem. TMZ broke the story ... she is about to be charged with lying to cops in June after her car accident on Pacific Coast Highway. She told them she was a passenger in the Porsche when actually she was driving.

And, if Lindsay is formally charged with the latest crime, it could trigger yet another probation violation.