We have a flight from Houston to LAX on Southwest (arrives 7:20 am at LAX) then an international flight on American Airlines that leaves at 10:50 am to Japan. If we have carry-ons only will we need to exit security and re enter?
Yes, you will. This isn't because of any aviation or security laws, but simply because Southwest's terminal at LAX (Terminal 1) isn't connect to any of the other terminals airside (post-security). You'll need to walk or take the shuttle to Terminal 4 or 5. You could also probably reclear security at the TBIT, but those security lines are horrendous. Best (usually) to go to Terminal 4.
Whether you booked your ticket under one leg or different tickets for both the legs, if the terminal is different, you have to check-out & check-in again to catch your next flight.
It's the case for both domestic & international flights.
- Check the arrival and departure terminals before you leave.
- Use Google Maps or Airport Map to know about the Terminals.
- Allocate Time for Check-Ins & Check-Outs (2 hours for domestic & 4 hours for International is usually required for security check-in, boarding pass, ID verification, luggage check-ins, etc).
- Research & find if there's any simple connectivity to reach the other terminal (in case of connecting flights).
- Take help of customer service & to move to other terminal, better take Airport Shuttles.
This wikihow article can be worth to read: https://www.wikihow.com/Switch-Flights-in-LAX