Citation II S2/Bravo Captain reported an engine malfunction during cruise. The flight diverted to an alternate airport and landed.

Narrative

On Day 2; I was flying a Citation from ZZZ1 to ZZZ2 on the way to ZZZ3 with the owner of the aircraft and another pilot who was assisting me. I was at 37;000' over Location X in intermittent IMC when the left engine rolled back from approximately 100% power to 65%. For approximately 15 minutes I went through troubleshooting steps including running checklists and noting engine parameters. The left engine remained at 65% despite these actions. As I was working through the situation; the speed of the aircraft gradually slowed and the angle of attack slowly increased. I asked for a lower altitude of 35;000' which ATC authorized. The engine was still not responding properly so I determined that a diversion would be appropriate to ZZZ; about 70 miles behind us to the West. I tried twice to make a radio call on ZZZ Center but the frequency was very congested (likely due to the extreme turbulence over the area that day and numerous diversions). Since the speed was continuing to decay and we were still in intermittent IMC conditions; I requested priority handling and asked to divert to ZZZ. ATC was very helpful and I got turned around and started to run our checklists to prepare for landing. While descending through 28;000'; the left engine power was restored. I wasn't sure if I should terminate the priority handling so I just continued what I was doing at that point. I landed at ZZZ airport uneventfully and debriefed with an airport official. In hindsight; I wish we had simply asked for a diversion earlier instead of priority handling as I only needed a precautionary landing to assess the situation on the ground.For additional context; this flight was conducted to return the aircraft to its home base in ZZZ3 so the engine could be evaluated by the appropriate maintenance personnel. The owner chose to accompany the flight after being informed of a previous engine-related event that occurred on Day 0. During the final leg of that flight; approximately 150 miles south of ZZZ1 the engine experienced a temporary power fluctuation before returning to normal operation within several minutes. The flight concluded in ZZZ1 without further issues. I communicated the event to the owner and the aircraft manager immediately upon landing. After being notified; they indicated their intention to have the aircraft returned to ZZZ3 promptly so the engine could be inspected by their maintenance team.