Depends on the type of lighting and how the bulbs are re-started. Many arenas have a mercury-vapor typoe lighting system, which produces a very white-bluish light. If the bulbs are turned off, they have to cool down in order to be re-started, and that can take a few to several minutes, depending on how long they were on when extinguished.
Many facilities are retro-fitting the lighting with a fluorescent based system, which produces the same lumens ( lighting units) but use far less energy. Kind of like replacing the standard bulbs in your house to the CFL curly bulbs, same light for less power. Tip for homes, start looking the LED based lighting, it is more expensive, but will last a long time and uses little power.
No matter what kind of lights, the "Cats will shine!!