you can get a taxi to the airport were you can rent a car. You need to know that traffic in LA is not like anywhere else. I live out side of LA and during commuting hours it is impossible to get around. Also it takes at least two to three hours before your plan leave to get through LAX.
LA is so screwy (and I'm a retired LA cop) that I wouldn't do it unless you really need/want to. I don't recall any car rental services in the terminal but I would suggest working backwards...check with a preferred car rental service to see if they run shuttles into the "World Cruise Center."
Maybe someone else remembers if they have the direct line phones inside the terminal?