Here is what the WN website provides for international flights. A recommendation of arriving at the airport at least 120 minutes prior to departure of the first flight with a deadline of checked in by T-60. Not sure where the 90 minutes comes from.

But, WN has no idea where you are in the world until you get to the front of the line to have your documents verified. I suppose that you can arrive at the airport at T-61 and pray that there is no line.

If your itinerary includes at least one international leg, we suggest that you arrive at the airport at least 120 minutes prior to the departure time of the first flight in your itinerary. Your passport must be verified by an agent or kiosk at the Southwest Airlines Ticket Counter at least 60 minutes prior to your scheduled departure time in order for you to be accommodated on your flight.