They don't close the water parks, but they will make everyone get out of the water and off the slides of there is lightning within an x-mile radius (not sure of the exact number).
We were at TL once when this happened and though the park was officially open, it cleared out very quickly even though they said it was expected to "re-open' in just a few minutes. We stayed, had lunch and waited it out. It took a bit more than a hour, but they eventually reopened all the slides and let people back in the water. There might have been a hundred people in the park they rest of the afternoon. It was great!
If it's just raining, everything goes on as normal, except there will be far fewer people there.
Steve