We've been there in the rain in the past. Everything ran except the parade. They moved the trick or treat stations inside and most of the activities inside. There wasn't any lightning though and that might be different.
In fact, one time several years ago there was a major storm front that went through at about 5 to 6 p.m. with tornadoes and everything. We were in our room; the front desk thought the party would be cancelled altho they hadn't heard anything official. But we saw on the weather that it was very concentrated and it appeared that it would pass through the area quickly. It was our only chance to go, so . . . we got on the bus with our yellow ponchos on (over the girls's costumes) while it was still pouring rain. I remember talking to another dad who was confident like me that it would pass through although we both were a little concerned riding the the bus with the rain coming down. Sure enough, it slowed down right about 7 - 7:30 p.m and actually cleared off by about 9 (stars came out). Because of the weather, no one came and it felt like we had the park to ourselves. No wait for anything. It was the most amazing night ever - very magical! Of course, it spoiled us for how crowded, relatively, it has since become. We still enjoy it though!