Kate Major Arrested Over Alleged Airplane Battery

11/7/2011 4:25 AM PST

Kate Major Arrested -- Alleged Airplane Battery at LAX

At the same time Lindsay Lohan was checking into jail last night ... her father's ex-girlfriend was also in custody ... after getting arrested at LAX ... TMZ has learned.

Kate Major was on a Delta flight from LAX to Tampa (sitting in 1st class BTW!) ... when cops say she battered someone on the plane around 11:45 PM.

Major was escorted off the flight and arrested for misdemeanor battery. However, Major was not taken to jail -- instead, she was simply cited and released around 2 AM. 

Law enforcement sources tell us Major was intoxicated during the incident -- but the booze was not a factor in the arrest.

We're told Major was on her way to Florida for a November 8 court date regarding her request for a restraining order against Michael Lohan -- the guy who allegedly beat her up last month.