We go every year in July, and the forecast always has T-storms in it. Like some of the other posters have stated, you never know in Florida! Bring your ponchos and have a rain plan. The T-storms typically come in the afternoon, and then the weather clears for evening. Go do some shopping or to one of the resort arcades if you're not planning to nap. If you're at the park, just go to rides or shows. Anything under cover will still be operating. If it's raining at night, Spectromagic generally won't run, but they usually don't make the announcement until the last minute. I think I can remember seeing the fireworks at MK in the rain last year. And Illuminations never is cancelled by weather. Last year we stood under cover and watched it in the pouring rain. It was pretty neat - almost everyone else had left because it had been raining all night so it was very easy to find a spot. And what made it really awesome was watching the lightning flashes during the show! I'm sure Fantasmic would be cancelled if it's lightening, but I don't know if there is just light rain.
Disney closes any pools or water parks the minute lightning is in the area. If you're at a water park, just get your hand stamped and come back later in the day. Chances are the park will have cleared some by then and the lines won't be as bad anyway.
You'll have a great time no matter what happens with the weather. Our very first trip was right after Hurricane Erin roared through, and it rained almost no-stop the last few days we were there. We still loved Disney so much we bought into the DVC and have come back every year in July since!