Yeah I thought about that, and initially thought it would need complex algorithms to solve, but there is a practical solution for it (come to that in a moment). But you mention that there are people that want to have all the alerts. That seems a bit crazy, that could generate hundreds or thousands of alerts. To those people I would say, as soon as the first alert comes in, open you app and just watch all the strikes come in, no need for further alerts. But for sure we love watching the strikes getting closer in the app.
In my opinion the purpose of the alerts is to alert people of incoming lightning so they can take appropriate action (go inside and enjoy the storm on your app 
). It would also be good if the app warns for lightning storm coming towards you, and not just passing by very far away.
So the idea in general is to give you a warning as soon as the app is confident that there is a strike (((a long time ago I already offered a solution to suppress the false strikes, but that might have been solved in a different way, or not, I don’t know))). Then if the storm gets closer and closer, send at most a handful of extra notifications and that’s it. No more notifications, you are in a storm, and better sit it out. It will pass over. if it is a big storm, the current implementation just starts sending new alerts half an hour after it send out the last notification. It wrongly assumes it must be a new storm. And you will get a series of notifications of strikes getting closer (but in reality it is the same storm not getting closer at all). Having a timeout after the last detected strike instead of the last reported strikes prevents that.
Now getting back to the situation that another storm enters the detection range without the previous one being gone. The fix to the problem mention above was to have a timeout after the last detected strike. That would assume that this is still the same storm and not notify you again. The solution to that is to have a time-out per range (the 4 or 5 ranges you mentioned earlier). So that is 4 or 5 timers. A timer restarts when it detects any strike in its range or in a range closer to you. You won’t get notifications for a range when its timer is still running. So if a strike is detected at 12 km, the timers for the range 10-20 km and 20-40+km would both restart.
@dsj if that isn’t a clear enough description we could discus in private.