Back in the day, I lost a computer from lightning. I was in the habit of shutting off my computer during thunderstorms, and naturally, I had it running from a surge protector, so I thought I was safe. What I had not realized at the time, was that my dial-up internet connection, which had a phone-line going straight from the wall jack to the computer, did not go through a surge protector, and was therefore an easy target, so to speak. Sure enough, lightning struck a telephone pole, which sent a surge right through the phone line and killed the computer, with nothing but a small black scorchmark on the end of the phone-line to hint at what had happened.
Having the computer flicker on and off with your lights is certainly not a good thing, so I'd reccommend shutting it off and making sure *all* possible routes to your computer are protected. However, this is one of those "Do as I say, not as I do" situations, as I stopped proper safety procedures long ago, and don't let the storms change my activities