The Zoom H1n has three settings that can affect recorded volume.
Auto Level, Page 19 of the manual.

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Noise, Page 21 of the manual.

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Limiter, Page 22 of the manual.

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Of the three, Auto Level can cause the problems you have.
However, setting the H1n to record thunder and rain will be a challenge. Rain sound (really rain hitting something) is nice quiet, even "pink noise" sound. Thunder is loud enough to move your shirt and it's very low pitch so you can't even hear about a third of it. My guess is you're going to get good recordings of one or the other. Get some good rain sounds and let the thunder overload. Then go back and set levels for the thunder.
Page 18 of the manual.

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...and mix them later in Audacity post production.
This isn't an easy recording job.
If I had to do this
in one pass, I would probably set one of the Low Cut Filters (80Hz) and then turn the limiter on, but not the auto level. That and record rain hitting leaves on trees, not your roof or the street. That gives a much more satisfying shshshshsh sound.
Fair warning, you're going to get a "Hollywood" thunder shower. It's not going to sound like it did when you were there.
It depends on your show. How are you listening? I have a killer sound system and powerful sub-woofer that can shake the wine glass. That's perfect for this job.
What is your show? Who's listening?
Koz