What was found
05/03/2019 FIRST FLIGHT JFK TO CAK A SHORT TIME AFTER TAKEOFF, I NOTICED A SLIGHT UNUSUAL NOISE (HUM OR BUZZ) AND ASKED THE FIRST OFFICER IF HE NOTICED ANYTHING. HE SAID NO, TO HIM EVERYTHING SEEMED NORMAL. THIS WAS VERY FAINT AND WAS NOT NOTICED BY THE FO. I DETERMINED AT THIS TIME THAT IT MUST JUST BE NORMAL FOR THIS AIRCRAFT. AFTER LANDING AND A SUBSEQUENT WALK AROUND, THERE WERE NO VISIBLE INDICATIONS OF ANY ABNORMALITIES. SECOND FLIGHT CAK TO JWN (DIVERTED TO KCVG) STARTED LT ENGINE PIC NOTICED SAME SLIGHT NOISE PREVIOUSLY EXPLAINED IN THE PRIOR FLIGHT. THE LEFT GEN DID NOT COME ONLINE WITH "GENERATOR OFF LEFT CAS” MSG. RESET THE GEN WITH NORMAL INDICATIONS. SUSPECTED THE GEN AS CAUSE OF THE NOISE. WITH NO FURTHER INDICATIONS OF AN ABNORMALITY, CREW DECIDED TO CONTINUE THE FLIGHT. THE NOISE WAS VERY FAINT AND STILL NOT NOTICED BY THE FO. LEVELED OFF AT FL430, THE “FUEL PRESSURE LOW LEFT” AMBER CAS MESSAGE AND “FUEL BOOST PUMP LEFT” AMBER CAS MESSAGES APPEAR. PIC CALLED FOR THE CHECKLIST, THE LEFT ENGINE LOST POWER, PIC PULLED THE THROTTLE TO IDLE, AND WAS DIVERTED TO KCVG FOR AN EMERGENCY LANDING. THE LEFT ENGINE WAS STILL RUNNING, JUST NOT PRODUCING FULL POWER. BEGAN LOSING FUEL FROM THE LEFT SIDE, PLACED FUEL TRANSFER ON RIGHT TO LEFT, HOWEVER, AIRCRAFT WAS LOSING FUEL FASTER THAN WAS TRANSFERRING. (BY REFERENCE TO THE FUEL QUANTITY INDICATORS).