I've done this many times. Assuming you have baggage to claim, go back up to the departure level. There are escalators and elevators. Go east towards United T7. You'll see a pedestrian bridge leading to the parking structure. Take either the escalator or elevator up to it and cross over the roadway. Then take the escalator up one level to the top of the parking structure. Go north towards Southwest T1. There's a bridge connecting the two parking structures. Cross over. You're now in the garage opposite Southwest T1. Keep going to the elevators. Take the elevator to the pedestrian walkway. Cross over the roadway. Go down to departure level. Voila! You are now at Southwest T1. Should take less than ten minutes. If it sounds confusing, look at LAX on Google maps and it will be clear.

More reliable than the inter-terminal bus. When time is of the essence, you can count on it to be late.