CE550 air taxi pilot reported during cruise experiencing left engine low oil pressure issue and fuel imbalance resulting in inflight shut down of the left engine. Flight diverted to the nearest airport where they landed safely.

Narrative

Engine oil had been checked at end of each fly day prior to this flight. Dipstick showed sufficient oil on each check. Aircraft flew from ZZZ1 to ZZZ with no abnormal indications. Aircraft departed at XA:42 from ZZZ. During climb out from ZZZ to FL330 LH engine showed slightly less pressure than RH Engine; but still within limits. Oil pressure slowly bled off inflight until it reached 40 psi. At approximately XC:10 the LH OIL PRESS LOW caution light illuminated with Master Warning light. Per emergency checklist; crew initiated engine shutdown; informed ZZZ Center; and began drift down descent to FL250. After discussing options; PIC (Pilot in Command) opted to continue to ZZZ1. When fuel imbalance reached approximately 300 lbs; crew initiated fuel transfer from LH tank to RH engine. While monitoring fuel level; crew observed RH fuel quantity continued to drop; while LH fuel quantity remained the same. PIC elected to divert to ZZZ2; which had just been overflown. Executed a single-engine approach and landing to Runway XXR at ZZZ2. After shutdown crew noted there was still oil on dipstick; although engine had only been windmilling. There was an excessive amount of oil in rear of engine (aft of turbine section) in engine exhaust area; not in bypass area.