B757-200 flight crew reported failure on both left fuel boost pumps in flight. The flight crew requested priority handling and descended to run the check lists and QRH procedures. The flight crew then proceeded direct to destination airport and made a precautionary landing.

Narrative

We were about 2 hrs into a 3 hour flight at FL410 when we noticed the left aft and fwd fuel pressure pumps lights both flashing on and off every couple seconds. There was no associated Engine Indicating and Crew Alerting System message at the time. As the situation progressed; the L AFT FUEL PUMP or the L FWD FUEL PUMP Engine Indicating and Crew Alerting System message would display for about a second and then extinguish. The Engine Indicating and Crew Alerting System message would display and then go out about a second later every five minutes or so. As a precaution; we elected to open up the cross feed lines to ensure there was adequate fuel pressure going to the left engine.We then discussed the situation and decided to descend to FL250 in order to improve our gravity/suction feed capability. By the time we got down to FL250; we had about a 1;000 pound imbalance on the fuel from the cross feed. We elected to close the cross feed valve and both left fuel fwd and aft pressure lights began to flash again. We watched the fuel flow closely and there was no indication of a lack of fuel flow; which indicated to us that the engine was receiving adequate fuel pressure through what we assume was predominately gravity/suction feed. The fuel imbalance stayed around 1;000 pound. We had the Quick Reference Handbook for FUEL PUMP Press and FUEL SYSTEM PRESSURE out and ready to run.We referenced both checklist; but did not run them because the pumps were intermittently working still. At this point; we were fairly close to ZZZ so elected to continue on ensuring we maintained situational awareness on runways nearby in the event the situation deteriorated or the left engine possibly flaming out. We declared a [priority] with ZZZ center and flew direct to the field for the visual to Runway XXC. As we passed through about 3;000 feet on vectors; the left fuel pump pressure lights stopped flashing and we landed uneventfully.