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.