To answer your first question above: Yes, you can all go via PreCheck together there. That approach is standardized nationwide, regardless of priority status with an airline.

At some airports in the Rocky Mountain and Pacific Coast time zones that have separate PreCheck and SkyPriority lines, those using the SkyPriority lines with a PreCheck boarding pass have been given PreCheck type screening after presentation of the PreCheck boarding pass to the TSA travel document checker. The way this works is the TSA TDC checker tells you to show the PreCheck boarding pass or a PreCheck access card (or both) to a TSA screener by the baggage scanner belt and then the TSA screener will enable getting screened like in the PreCheck line despite not using a dedicated PreCheck line. I�ve not seen LAX work this way for DL flights, but it�s been the case with DL flights out of other airports in California and states in the same or the neighboring time zone.

When I�ve had SkyPriority boarding passes I�ve been able to take my family members in with me via SkyPriority lines regardless of what their boarding pass states. But LAX may be more of a stickler about �coattails� when it comes to SkyPriority lane use than other airports.