The thunder, I understand. My dear departed kitty, was also afraid of thunder and he weighed 25 pounds! It's the sudden, inexplicable noise, I think. :-)
The lightning doesn't bother her, but the rumbling does.
Seems she was put in a burlap bag and tossed over an 8 foot tall fence into the Humane Societys backyard during a thunderstorm.
Also, she doesn't like being picked up for the same reason.