The best replacement for thunderstorm is lightning storm.

The best alternatives to thunderstorm are rated as following:
★★★★★  lightning storm
★★★★  thundershower
★★★★  thunderstorm
★★★  scattered thunderstorm
★★★  tornado
★★  shocking aspect
★  thunder shower
★  isolated thunderstorm
★  thunder storm
★  tornado strike
★  scattered

Your alternative for thunderstorm is not listed? Suggest!
Speaking about thunderstorm, one probably shouldn't forget about hail.

Other search terms related to thunderstorm and their ratings are:
★★★★★ hail
★★ tornado
You have in mind a companion for thunderstorm and it is not yet here? Propose!



Google Trends

Scale is based on the average worldwide traffic of thunderstorm in all years. Click on graph for more.
thunderstorm
lightning storm
thundershower