From staples center i would suggest u going 110south to the 105 west...it's way faster than going 10west to the 405 south as that is a detour....not speaking the 10 west traffic is going to be bumper to bumper by 6.30ish
another route u can use is 10west and exit la cienega....and drive south all the way to the airport....that's mostly local but shouldn't take u more than 30 minutes