For business class, they will send an agent to wait for you right out of the door of the plane, then they will use the pass to override the line for security check. At least for Cathay. Take Cathay serveral times, twice I have to have an agent to help me go through the secu line.
Before your first flight, pls check if your flight to LAX will be late, if you are late, then you can call LAX Eastern China to change the flight, but pls makge sure they have multiple flights.