Set up a motion sensor to turn on lights and record how long the lights are on
I would consider placing a light sensor close to one of the lights to signal when the lights are on. Placement is critical as you do not want a signal when the lamp is off. I am assuming they are permanent light fixtures and you are not allowed to tamper with the wiring.  Record the elapsed time when they are on.  Note the start time and then subtract that from the current time based on your watch. For elapsed time and subtract the ontime from that. With the sensor you can also record each time the light is turned on etc. That would all be in your software.