B757 Captain reported returning to departure airport after experiencing loss of power in the left engine.

Narrative

At ZZZZZ; we were at FL 380 when we heard a bang then a quick yaw and saw the left N1 vibration was in the amber band at 3.7. Ran the engine vibration checklist. We reduced the left throttle until it was out of the amber band. Huge split between the throttles. The left engine was operating at reduced thrust. Jointly made the decision with Dispatch and Maintenance Control to return to ZZZ with the understanding that if we had to shut down the L engine; we would divert to a closer airport. When we were at FL250; and we were in and out of icing- we got the L ENG ANTI ICE amber EICAS which was written up the night before when Aircraft X air returned and on the Aircraft X the left engine had been replaced. It was an ETOPS verification flight. We were in and out of the ENG VIBRATION checklist and did a flaps 20 landing. We briefed the flaps 5 go-around. We tried to push the GRD PROX FLAPS OVRD; but it did not take. We briefed that we would continue the approach when we got 'too low flaps' aural warning.Need to add that we tried to press the GRD PROX FLAP OVRD switch due to flaps 20 landing per the engine vibration checklist; but it did not take. We briefed to continue the approach when we got too low flaps aural warning; because we knew why. It was NOT an overweight landing. Our weight was 191# approximately.