1) Do the lights use energy, and 2) do they take that energy from the batteries that are the only source of power for the aircraft, and 3) do those batteries also supply power to the control electronics and motors?
Yes, yes and yes.
So, the lights reduce the flight time by some (probable) small amount as mentioned by others.
If you are going to cut the flight time that close, you my want to invest in a
Marco Polo lost aircraft radio tracker to help you recover your crashed and/or lost aircraft from the tree it’s hung up in. Here’s a link:
We build the Ultralight and Advanced drone recovery systems. These drone tracking and recovery solutions possess up to 15 days of battery life per charge.
eurekaproducts.com
Also, if you are flying FPV and need long flight times, consider buying a less expensive hexacopter that can carry bigger batteries, or better yet a fixed wing RC aircraft with a head tracking FPV camera. A motor glider will have the longest flight time if you use thermals on a sunny day. On a good, sunny day, flight times can last longer than you can. You’ll have to learn to fly a motor glider, and you may need both fixed wing and multi-rotor aircraft so you can fly in a wider range of weather.
Maybe put radio trackers on the sheep and learn how to use radio direction finding techniques to track them down. Check out the Marko Polo units and Google “Radio Direction Finding Locators” for other solutions.
In any case, best of luck!