I noticed when operating Field Day this year that during a period of rain, the RF background noise went up as well, from about S2 to S5-6. I was operating inside a tent, with the antenna outside the tent. It got me thinking though, is there things that I can do to a home station to keep the RF noise down during a rainstorm?
Not really. You can try using the noise reducer control on your radio, but if the noise is really bad, it won't be that effective. Most of the noise you're talking about was due to lightning near where you were operating. Not much you can do about that.
Magnetic loops are resistant to RF noise so may be a good choice in a wet environment. Also, using coaxial fed antennas instead of ladder line will reduce rain related issues.