There has been already discussions about the question of this density:
Is it per hour or per day?
The thunderstorm layer is expressed in lightning per square kilometre. It is the average density of likely lightning strikes computed on a wide area but then expressed per square km. So it is not within a radius to your location, just a potential density.
To clarify these 2 questions, see more detail from ECMWF about this parameter:
Finally I understand that ECMWF compute the potential of lightning strikes density during 24hours but they are displayed at a precise hourly time frame. It is about the same when you are driving, your speed is expressed in km per hour (or miles per hour), but your speed may vary by each minutes.