If lightning is around, DON'T wait until the storm is on top of you as you might get a strike out of the blue (sorry, pun not intended) as you are unplugging things.
I doubt a surge-arresting socket will help unless the storm causes a power surge by striking overhead supply lines. But, as they are so inexpensive, it's a good precaution.
It's more likely to get hit if you have a drop-wire connection rather than an underground telephone wire.
The chances of a direct strike are remote, but there will be considerable radio frequency high-energy pulses which are more likely to cause problems.
If there is a direct hit, the Router will be the least of your problems. Also, don't use the telephone if its directly connected to the line as you could get zapped too. DECT phones are ok as they connect wirelessly.
Allergy Advice: This post may contain traces of Meerkats.