ACR DEP FROM JST REPORTED RWY LIGHTS WERE TURNED OFF DURING TKOF ROLL DURING TWR OPENING PROCS.

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IT WAS THE FIRST FLT OF OUR DAY DEPARTING JST EARLY IN THE MORNING. THE FIELD AT THIS TIME WAS ON CTAF BECAUSE THE TWR WASN'T OPEN YET. WE WERE TAXIING OUT TO THE RWY. WE TURNED ON THE PLT CTLED LIGHTING AND PROCEEDED TO THE RWY 23 MAKING OUR TFC CALLS. THIS TOOK APPROX 5 MINS FOR US TO TAXI AND PERFORM OUR CHKLISTS. WE MADE ANOTHER TFC CALL; GOT CLRNC FROM ZOB ON 121.2; AND TOOK THE RWY FOR DEP. WE THEN MADE ANOTHER TFC CALL AND STARTED THE TKOF ROLL. JUST AS WE HIT OUR DESIGNATED V1 SPD; THE FIELD LIGHTING SHUT OFF. AT THIS SPD AND BECAUSE WE HAD WHAT I DETERMINED TO BE ADEQUATE VISIBILITY; WE CONTINUED THE TKOF. AFTER WE FINISHED OUR CHKLIST AND WORKLOAD PERMITTED; I CONTACTED JST TWR WHO WAS NOW OPEN AND TOLD THEM WHAT HAD HAPPENED. THE CTLR ADVISED ME THAT THEY HAD NOT NOTICED; BUT AT ABOUT THAT TIME THEY HIT THE 'PLT CTLED LIGHTING SWITCH' WHICH SHOULD NOT HAVE TURNED THEM OFF; BUT THEY WOULD CHK INTO IT. I AM NOT SURE IF THIS WAS JUST A TIMER ISSUE FOR THE LIGHTS OR IF THE TWR ACCIDENTALLY TURNED THEM OFF. THE FLT CONTINUED WITHOUT INCIDENT.