Answer
A car burns more gasoline when its lights are on. More energy is being output and consumed, so more energy must be provided.
Energy from gasoline may be temporarily stored in the car's battery to power the lights when the engine is not running. Ultimately, all of the input energy comes from gasoline, so it doesn't matter if the engine is running when the lights are on.
A engineer who is being nitpicky may argue that the storage process is inefficient, so one uses marginally less gasoline when the engine directly powers the lights, but this is a negligible effect.