The NTSB report called it a military airbase, and other reports say “Military air traffic controllers guided the aircraft”. Civilian aircraft can use the military side with a permit.
Plenty more info on the air field at https://military-history.fandom.com/wiki/Lajes_Field
Lajes’s other claim to fame is that Bush and Blair met there just days before the Iraq invasion to hammer out whatever deal they thought had to be dealt.
The tale of the stricken aircraft was fascinating. I’ve always wondered, over the decades as I’ve flown slight doglegs over Earth’s oceans, if the strategy to route over remote airfields in case of emergency has ever had a “cost” estimated. How many hours and gallons of fuel has been spent for this safety blanket? The infrastructural insurance spent to prevent lives lost in air travel appears to be much higher than lives on road travel. Could it be that the insurance is for the aircraft, not the lives? Hmm.
The island, and the others of the Azores, are a wonderful place to visit by the way.