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

During climb out through about 10000 Ft we got a L oil press low warning CAS message. The oil pressure dropped to zero and then quickly climbed back to the normal range. We monitored the indications from the left engine and all other parameters looked normal. So the message was cleared and the flight was continued. Then the L oil press low warning CAS message returned and again oil pressure dropped to zero and then quickly climbed back to the normal range. When it happed a third time and the oil pressure stayed at zero; we reduced power on that engine and notified ZZZ Center that we would like to return to our departure airport (ZZZ). During that process we started the L oil press low checklist. Once cleared we initiated the turn back toward ZZZ and in that turn we felt and heard a loud sound from the left engine. After that we requested priority handling and through the checklist we shut down the left engine. Once the engine was shut down we communicated with ATC through our return to ZZZ and landed safely on Runway XX. Once on the ground we taxied to our hanger on the airport. Cause: Mechanical failure of an engine part that allowed the oil to leak out from the left engine causing the L oil press low warning.Suggestions: At this time I don't know if that can be determined. We should have more information once maintenance has a chance to inspect the engine.