Air Traffic Controller reported an F35 aircraft experienced a complete electrical failure resulting in the aircraft landing at the first available airport.

Narrative

Aircraft X was at 370 negative rvsm. The pilot called and requested lower immediately without more information. I couldn't give lower because they weren't in my airspace yet and there was traffic climbing to 350 underneath them. I was able to get up and go across the room and coordinate with sec XX and XY for lower. I gave the aircraft as low as I could traffic permitting. Sec XX turned the aircraft that I wasn't talking to yet climbing underneath to give us more room. She kept asking for lower and I simply gave her the traffic update several times that was heads up with them. I didn't want to turn them yet until I knew the nature of the situation. The pilot [requested priority handling] and descended down to 170; I was able to give them an altimeter and sector XY coordinated with ZZZ approach for lower. I called the nearest airport that I thought they could possibly land at. I wasn't sure if a F35 could land at ZZZ but I thought it could be a possibly because they have the F16 squadron there. I was going back and forth to from XZ-XX-XY to look for limited targets that I couldn't see from the XZ scope. By the time I got back the aircraft was down to 170 in a minute or two. I coordinated 150 with ZZZ approach and shipped the aircraft to them. It all happened extremely fast and we did all we could to move all traffic out of the way to accommodate them. The pilot later stated it was a complete electrical failure.