Okay, first off, you'll be just fine during a thunderstorm from lightning if you do the smart thing and take shelter when a storm hits, not use umbrellas, etc. If you follow the steps people here have pointed out, you'll be
fine.
Now, I say this because what I'm about to tell you might make you freak out and forget all that, but
REMEMBER IT. What happened to me was a
freak occurrence and has never happened since to anyone in my family that has visited WDW. I honestly just find this to be an ironic time to tell the story, because it's so fitting. But seriously, don't worry.
Late May/Early June of 2010, my family and I were visiting HS, and we were just about to leave the park because of both a storm approaching, as well as getting dinner at WL. We had just left Muppet Vision and were about to approach Echo Lake when we see VERY dark clouds coming up, the ones so dark it would make a sunny day at noon look like night. It's thundering and lightning, and it had rained earlier from a different little system, but we kept going. Just as we start to pass Echo Lake (I'd say no more than 30 yards away or so at the most), a bolt of lightning struck one of the palm trees, causing its bark to explode off and some of its leaves to come tumbling down to the water while on fire.

There was obviously no delay in the thunder since we were so close, so it was a sudden CRASH explosion sort of sound, and we almost fell down from the shock. Imagine how a typical crack of lightning sounds, and multiply the sound/effect by 20, that's how impressive it was!
There weren't many people around, and it wasn't raining, but all of a sudden my niece and SisIL were freaking out, sobbing from how fast/loud/destructive it was (which I totally understand). The air also felt so strange, like it was alive from the electricity. Some of the bark that had exploded off the tree was just floating in the air, from both the wind moving it and (what I can assume is) the electricity it was surrounded with. It freaked us out, that's for sure, and we made sure to hightail it outta there as soon as possible afterwards! Of course now we can look back on that and laugh at how crazy it was, but at that moment it was pretty nerve-wracking.
Okay, so I hope I didn't freak you out. This was a freak occurrence that I don't believe happens to that many people in Disney, so I think you'll be fine. Just watch the weather, get yer ponchos ready, and
stay clear of palm trees!
......and yes, this really happened.
