It's quite understandable really. She is at the age where she understands that Mommy and Daddy have NO control over the weather, and that the weather is a powerful (and yes downright scary) force. It doesn't have feelings, it just IS. That is a scary thing for a 6 yr old to contemplate.
You could pull out some statistics maybe (real plain ones... # of people struck by lightening last year in YOUR state, number of tornados in YOUR state, number of flood related drownings in YOUR state, etc and compare it to the number of times it rained in YOUR state, or even in your town. It might help her see how UNlikely it is for something bad to happen.
Also, you can try to give her happy warm feelings about rain. I remember as a kid getting out the sleeping bags in the living room with my brothers and watching TV and reading books and things. We even made tents out of blankets/sleeping bags draped from the back of the sofa to chairs pulled out into the room, and things like that. It was all cozy. It'd be SUPER easy to do today-- pop in her favorite DVD, make some popcorn and snuggle down with her under a blanket tent.. lay on pillows on the floor!
Make it a special time, and try not to focus on the rain itself. Make it about spending time with HER. Tell her what YOU like about the rain. I personally LOVE the rain... I still love being under a blanket on the sofa with a good book when it is raining outside.
I don't care much for lightening storms... but as long as everyone is away from the windows.. it isn't bothersome unless it is REALLY REALLY CLOSE!
Just remember that if YOU behave stressed, or you worry about the weather, she is going to hone in on that vibe, and she will be more worried. Try to be relaxed, and make jokes about something unrelated, act silly, and if she still is freaked out, be matter of fact about the facts... "it is very unlikely that anything bad will happen, even if we went outside and stood in the rain (except we'd get really wet and have extra laundry to do). That doesn't mean we stand in a big open field during a lightning storm, because that isn't what you do in a lightning storm. You stay inside away from windows. But we don't need to hide from just rain. It's just water. Our bodies are 95% water." (isn't that the right percentage? lol). You get the idea. Maybe you could take her outside in a light rain (when it is just rain and no lightning, of course) with an umbrella and let her splash in puddles. My kids LOVED doing that when they were younger. It is messy.. but it's a memory maker... and if she will do it, it might help her see another side to the rain.
Hope this helps~