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.

Hopefully Lindsay can get her life in order.

And Michael does not need to be having anymore kids

Another kid?

Haha, was he even a father to the first batch?

She is so lucky, I mean hasn't she gone to court like 15 times for the same thing?