To reproduce:
You must not start your initial flight from KLAX.
KLAX needs to be your destination only. Selecting KLAX from the XPlane Menu as a starting point (at gate or on runway) will not cause any issue.
When arriving at KLAX (assuming it is set as you destination, no matter where you departed from) upon opening the SAM3 Menu, on the Arrival tab, it is impossible to select arrival gates as the airport shown on SAM would be 9L6.
I have personally tested this on a round trip, starting from KLAX to KSAN
KLAX KSAN - No Issues upon departure, SAM worked perfectly well.
KSAN KLAX - Everything went as planned at KSAN, however upon arriving at KLAX, SAM would still not recognize KLAX and would detect it as 9L6 again , thus preventing from unloading/docking at the gates.