Our trip is planned for June 16-23 and I know it rains in Florida a good bit. I’ve been to Miami in the summer and it’s usually a downpour for about 20 minutes and then it’s done.
Does that tend to be the same in Orlando? Also, do rides shut down if it rains or just lightning?
from what it looks like, most rides continue in rain. Lightning…not so much.
Do you know if lightning is AS common as the rain?
Most rides continue in the rain - it is thunder that is a problem.
Some rides shut down just for lightning in the area (5 miles away), yet it’s not raining at all at the park. We had that happen in July when we wanted to ride the railroad at MK. There were a couple times (Sat evening and Monday afternoon) when it was heavy downpours that lasted quite awhile, maybe closer to half hour or more. Other days, it was just a light sprinkle.
So it appears that it is a daily incident? 
No, there was actually a day or two with no rain at all. It’s very hit or miss. Often a daily risk of showers, but the actual rain varies widely. Therefore the common suggestion to usually carry rain ponchos (the lightest, cheapest ones from Walmart or a dollar store work great). I don’t think rain was a big impact on my day’s schedule. The evening fireworks show at HS was delayed, not cancelled.