He shouldn't get stressed too much. Lufthansa/Swiss are rearranging their schedule a bit, due to decreased demand. And yes, this will mean that some flights are cancelled. That does not mean that all flights are cancelled or that they won't take him at all.
He has a ticket with Swiss, and they have to transport him to his destination, even if on a different flight. He does not have to worry about being "left behind" if he doesn't make his first flight.
Is the flight cancelled?
Currently, he does not know. He can (and should) check the flight status online (Swiss timetable and Lufthansa Flight Status).
As long as the flight isn't officially cancelled, it makes little sense to call or go to the airport - they can't tell you much. Also, it makes little sense to re-book if you don't know which flights are going to operate.
What happens if it is cancelled?
If the flight is cancelled, the airline will offer to re-book him on a different one: There are multiple flights from Athens to Zurich, but they could rebook him completely (e.g. going through Frankfurt on Lufthansa). If isn't happy with the new itinerary, they will usually offer other options. He could also get a refund, but it seems like he wants to travel.
If he booked it through a third party (e.g. Expedia), he'll have to go through them for any re-booking.
If the flight isn't cancelled, he should be at the airport early so that he can directly talk to the agents in case of a last-minute cancellation.
On their information page Swiss currently informs passengers that they can freely re-book all tickets bought before March 5th. (However, it seems like your BF wants to travel).
In case of a delay or cancellation your BF may also have a right to compensation under the EU rules - at least in this case, when the outbreak directly the reason for the cancellation.