When the airport is closed, in case there was an emergency that needed to reroute. One person on then makes sense?
La Guardia appears to handle 400 flights a day, 22 an hour. I see 6 moving planes right now (https://www.flightradar24.com/airport/lga); hopefully they have more than one person on?
400 flights a day is 16-17 per hour and those are going to be mostly during the day. As someone else points out there is a ~6 hour stretch overnight with no scheduled departures. That's somewhat common even at large hubs.
I don't want to blow your mind but if the airport closes there aren't going to be any controllers in the tower.