I have quite often booked flights, with United, and not used the last portion of a flight. I usually inform the check in agent that I do not want to use the last portion. I then have to sign my baggage tag, to say that I have asked not to use the last portion. My bags are then only sent to the penultimate destination.
If you have only hand luggage, technically you wouldn't have to inform United. You could just walk off. It may be an idea to inform them when you get to LAX.