Lindsay Lohan -- I've Got a New BABY BROTHER!

Big day for Michael Lohan ... his daughter escaped jail ... and his fiancee just gave birth to a BOUNCING BABY BOY!!!

While Lindsay was sweatin' it out in court, Kate Major went into labor at a Florida hospital.

We're told Kate gave birth to a son -- Landon Major Lohan -- at 11:39 AM PT.

The baby weighed in at 19 3/4 inches, 7 lbs 5 oz ... and is already wanted in 3 states (kidding!).

We're told Michael was with Kate the entire time ... and even cut the umbilical cord.

A rep for the family tells us baby, Michael and Kate are all doing great.

Congrats!!!