I had my AS connected to my home power charging the batteries prior to our last trip, There was a thunderstorm and a nearby lightning strike. The only thing damaged was my parallax powerconverter in the AS. This turned out to be a rather expensive fuse. I went to camping world and picked up a replacement power converter - and - a surge protector.
The surge protector's job is to protect the AS from sudden high voltage spikes, way above the normal power line voltage. These spikes can come from nearby lightning - it doesn't have to hit your home transformer it could be nearby and couple into your home wiring. Or they could come form other equipment in your home or on the same circuit as your home that is switching a large electrical voltage or current that puts a very short pulse of high voltage on the line.
This very short bursts of energy can be coupled into the electronic devices and easily destroy the electronic circuits. Generators that have a square wave type output could also create high transient voltages due to the high frequency components in the square wave.
There are a couple of ways to prevent damage. Filters, which reduce the high frequency components and keep them from getting through to your electronics, and surge protectors which can reduce the amplitude of the voltage spike.
Most of you have seen small filters on your computer cables as small round plastic tubes that are clamped over the cable. They contain a ferrite washer which will add inductance and tends to slow down those fast moving voltage spikes, Inductors and transformers like their electricity to be slow and steady.
Most laptops today come with switching power supplies that can adapt to the line voltages of various countries. That is good for transient protection as well because the filter at the output of the power supply is designed to suppress the voltage transients caused by the switching converter.
My own preference (learned the hard way) is to use a surge protector between my RV and the power source to protect the electronics in my power converter and refrigerator. The one I purchased has a built in ground fault interrupter which can protect me against unintended electrical current paths to ground.