Citation Captain reported during the climb experiencing left engine low oil pressure warnings resulting in the flight crew returning to the departure airport where they landed safely.

Narrative

ATC issued us to climb to FL310. During climb thru approximately. 12;000 ft.; the Cab Alt annunciator warning illuminated. I acknowledged the warning and confirmed the cabin altitude had risen above 10;000 ft. I then requested ATC that we level off at 13;000 ft. since that would be our next altitude to capture with the Autopilot engaged to address the issue. We pull the abnormal checklist. Since we were leveling at 13;000 we did not elect to don oxygen masks or switch to mic oxy mask; and an emergency descent was not required. Per the checklist; we checked the PRESS SOURCE Select Knob and confirmed it was in the NORM position. Next the condition of the passenger was normal. Next was to request priority handling by setting the transponder to 7700.I have experienced a pressurization issue in this aircraft a couple months prior; which required an emergency descent. I confirmed with the PF and opted to go ahead and request priority handling and return to the departure airport. We were not overweight and requested we enter the traffic pattern for landing. We began our descent and landed without further incident.I contact our company to troubleshoot the cause of the issue. We were parked on the ramp nearest the parking lot which provided adequate lighting in the cockpit to reveal the Press System Select switch was in the Manual position. The aircraft should be operated in normal operations with the Press System Select switch in the Auto position. This switch is not guarded.I suspect the state of the Press System Select switch occurred during engine startup at the beginning of the flight. In the Citation Bravo; we typically start the first engine with the battery; then start the second engine assisted by the operating generator. In order to conduct a generator-assisted start; the Ground Idle switch must be placed into High. The location of the Ground Idle switch is adjacent to the Press System Select switch. Furthermore; we have a PIC (Pilot in Command) in training going through IOE. I elected to let him sit in the left seat and conduct the flight as PF (I was PM). Engine starts are conducted from the left seat. It's possible that the Press Select Switch was accidentally placed into Manual while selecting the Ground Idle switch to High.In hindsight; the state of the Press Select switch in Manual was missed due to:1. Placement of the switch located next to the Ground Idle switch; near the thrust levers.2. Night operation and poorly illuminated cockpit.3. The company issued checklist does not have the crew check the status of the pressurization system prior to departure.4. The manufacturers abnormal checklist does not specifically verify the position of the Press System Select switch; only the PRESS SOURCE knob on the other side of the panel. 5. Crew placement during a live leg (PIC in right seat; PIC-in-training in left seat).SuggestionsRecommend adding a pressurization check prior to takeoff to our company checklist. The manufacturer normal checklist has a pressurization source selector check in the Taxi checklist. I recall when I first started with the company; we would use a version of the manufacturers checklist and the callout was 'Auto; Normal;' indicating a verbal check of the Press System Select switch is Auto; the PRESS SOURCE knob is in NORM. Illuminate the cockpit to reveal the condition of switches on the panel during night operations. Also recommend we share events internally with other crewmembers so we can learn from each event. I have since found out that another crew had a similar event but quickly rectified the situation as they discovered the same switch was in Manual; but it was during daylight hours.