Captain reported an in flight engine shut down and a diversion to make a precautionary landing after a previously reported excessive ITT problem on the left engine reoccurred.

Narrative

Had an airplane that was written up previously for ITT exceedance on the left engine when set to climb thrust and had to fly with reduced thrust rest of the flight. On my flight in this aircraft prior to this event I also had same thing occur to me and when we got on the ground and maintenance came they said it was all good. During my brief with my First Officer we talked about taking precautions and being easy with power and monitoring the ITT in case it would occur again and so as to not exceed. During the climb out I did keep the power back a few percent in case; but no ITT exceedance nor any other indications. We make it to cruise and are about 45 minutes into the flight; left ITT spikes and flashes red; can feel and hear the left engine sputter and the N1 drops and stays about 30% with a left engine oil warning. I ask my First Officer to run the QRC for engine fire/severe damage in flight. ZZZ was right nearby; they got a long runway that match up for the general winds; and VFR. We exchange controls and I set my First Officer up to head to ZZZ and ask ATC to put us in a hold or box vectors as we continue the descent down. I call my Flight Attendant and brief her what is happening up front and ask her to check the engine and see if she happens to see any smoke or damage. She says there is none and I let her know we are diverting to ZZZ and if she could make an announcement to the passengers. I run the QRH; left engine is shut down and secured; and I brief my First Officer the approach and the differences to the landing. We exchange the controls; land and stop on the Runway and make my announcements and call my Flight Attendant. I had emergency personnel verify no smoke or anything was to be seen from the outside; and decide to continue under our own power to the Gate. Not sure if maintenance really looked to see what the reason was for the high ITT; they just said that the engine was okay and that ITT was within limits and good to go. After two occurrences perhaps take a closer look for the reasoning and see if there is some sort of issue with the engine.