A Falcon 2000 Captain reported they shut down an engine and diverted due to loss of oil pressure indication. The pilot reported 'the oil cap was not in the original place'.

Narrative

Below I will explain the events that occurred on the flight ZZZ1 to ZZZZ2 and the diversion to ZZZ3 on Date 2. We departed from ZZZ1 Airport at XA:22 UTC. Climbed to FL430 and later to FL450. At XB:35 into the flight the light of 'Low oil press' (red light) began to flash. In between; we started to see fluctuations in the oil pressure and turned to the Quick Reference Handbook 'OIL PRESS'. The pressure went down from normal 54 PSI (yellow arc). We decided to land in the nearest airport which was ZZZ3 with the left engine in IDLE. We informed the ATC [and requested priority handling]. We initially were at FL450 and were given an initial decent to FL380. As we started our approach and descent to ZZZ3; at between 7000 ft. and 6000 ft.; the oil pressure dropped below 30 PSI for which we proceeded to turn off and secure the engine via Quick Reference Handbook. The approximate time with the engine off was 10 to 15 min. Approach and landing with one engine inoperative was performed. We were able to land safely and no issues upon arrival in the ZZZ3. I have a logbook entry prior to the flight showing the engine oil was serviced. On Date 3; I now learned that the oil cap was not in the original place. The aircraft has now been returned to service. Time of Engine in Idle [was] between 30 and 35 minutes. Engine Time Off (windmilling) [was] between 12 to 15 min. Oil press" reading at the start of the flight [was] Arco Verde. [The] engine reading in Idle [was] 54 PSI [and the] engine reading off [was] 0 PSI. [The] flight level at the start of the event [was] FL 450. [The] fuel remaining on arrival in ZZZ3 [was] 6500 lbs. [There were 5 total] people on board. [The] Landing Weight [was] 30300 lbs. (Vref 121 k). First Level required at the beginning of the [incident was] FL 380. [My] latest recurrent training [was] Date 1. Any further information needed please do not hesitate to contact me. The Log Entry and Work Order showing the maintenance work done prior to and after the flight is available for your review if needed."