Firefighting pilot reported engine failure resulted in a return to a safe landing.

Narrative

We were Dispatched to perform a reconnaissance of the fire and once completed planned on performing a lightning reconnaissance. We completed work over the fire area and I advanced the power to initiate a climb for the lightning reconnaissance. The left engine responded normally but the right engine did not respond to power lever inputs either positive or negative. All engine indications were normal and no adverse indications on the right engine (no noises; vibrations; or leaks). I decided to return to ZZZ tanker base. Over the next 30 seconds to a minute the right engine power slowly decreased and I decided to perform a precautionary engine shutdown of the right engine and requested priority handling with ZZZ Approach Control. We were handed off to ZZZ Tower and cleared to land on Runway XX. During landing gear extension the right main landing gear and nose landing gear indicated down and locked but the left main landing gear did not indicate down and locked and was observed to be hanging about halfway down in the trailing position. I initiated a go-around and slowed the airplane to about 110 KIAS. The hydraulic pressure indicated about 1100 psi. The left main landing gear slowly continued down and eventually indicated down and locked. This was verified visually from inside the airplane and by the Tower. The flaps operated normally and I selected 1/2 flaps for the single engine landing. I then landed uneventfully and taxied to parking.