Lear 35 Captain reported erratic ITT indications; a right engine flame out; and an unresponsive throttle at idle on the left engine; led to a dead stick approach and successful landing at a nearby airport.

Narrative

I was assigned a non-patient MEDEVAC positioning flight using Learjet 35 Aircraft X to go from ZZZ1 to ZZZ2. I placed a fuel order with the desk at the FBO asking for a top off and positive for PRIST. I observed the counter person write 'T/O +' on the paperwork for the airplane. I proceeded out to the aircraft and observed the fueling. A total of 674 gallons was uploaded to the aircraft for a total of 6100 pounds of Jet A indicated.Takeoff was at XA46 hours; and the climb out was normal. We leveled off at FL350 and the aircraft accelerated normally to cruise speed 19 minutes after takeoff. Approximately 30 minutes after takeoff; the left Interstage Turbine Temperature (ITT) gauge starting indicating erratically between 0 and 750 degrees. All other engine indications were normal and both N1/N2 did not vary. Since the gauge did not have an OFF flag; I assumed the transmitter from the engine was at fault. The right engine started having small variations in ITT about 2 minutes after that. Approximately 1 minute later the left fuel flow indicator began displaying noticeable variations with small variations in N1/N2. The right engine variations became significant causing yaw issues. The QRH checklist was reviewed and appropriate steps for abnormal engine indications completed; as well as for engine failure and single engine landing.When the abnormal indications began on the right engine; we informed ATC we wanted to return to ZZZ. The Controller gave us an immediate left turn. The variations in the right engine got worse and the engine appeared to go to Idle. Shortly thereafter; the fuel flow indicator for the right engine indicated 0; indicating the engine flamed out. We advised ATC that we would be unable to maintain altitude and would be descending. ATC provided an immediate clearance to descend. An engine relight was not attempted because we were outside (above) the restart envelope indicated in the checklist.Passing through FL300 the variations on the left engine were increasing. We performed the procedure for abnormal engine Indications and restart of the right engine; but the engine would not start. The left engine variations continued to increase with a slow decay in the maximum N1. The engine was unresponsive to thrust lever movements in either the Computer ON or Computer OFF mode. We advised ATC we would make an immediate landing at the closest airport (ZZZ) passing FL270.Passing FL200 the left engine was now at idle. Thrust lever movement had no effect upon the engine. I began dumping fuel in an attempt to get to a normal landing weight. Passing approximately 12;000 ft. we got clear of an overcast and saw the airport. ATC cleared us for a visual and asked us to report on deck (uncontrolled airport). The controller advised us the winds were calm. I secured the dump switch. I was unable to transfer fuel from the full trunk at a sufficient rate to get to below 3;900 pounds (maximum fuel for landing).I elected to land on Runway XX and assumed I had zero thrust available from either engine. I continued the visual dead stick approach. On short final I lowered the landing gear at approximately 220 KIAS when I felt confident I could make the runway (I was intentionally high and fast at this point). I called for flaps 8 at 200 KIAS. After stabilizing and sure of making the runway; I called for Flaps 20. On very short final I called for Flaps 40 at about 160 KIAS. Touch down was at a slightly higher than normal speed; landing slightly long and using moderate braking to come to a stop about 650 ft. remaining from the end of the runway. After stopping on the runway; I noted the left engine was at idle and unresponsive to thrust lever movement. The right engine was inoperative. We landed with 4;100 pounds of fuel (15;500 pounds landing weight). ATC was advised of our safe arrival after touchdown.ZZZ is an about 6000 foot runway at an elevation around 4300 ft. The actual winds on landing were 300 at 8 kts. The estimated post flight calculated landing distance was approximately 3;900 ft. Post flight inspection of both engines revealed no visible damage to either engine.