Does this usally happen in Minecraft?

Minecraft has various weather effects, like rain, thunder and lightning, snow, etc.

OMGZ That's a sign that your game is haunted by slenderbender. He's slendermans gay brother. You must throw away your computerz now! Ever heard over the white dressed woman that haunts games? Look it up.

It's called weather bro…

It's not necessarily common, but Minecraft does have rain, or snow if you are in a 'cold' biome.

Rain puts out fires, and allows monsters to spawn even during the day.

Thunderstorms, like what you mentioned, are rarer and more dangerous than normal rain. In addition to rain's normal effects, you or mobs might be struck by lightning. It does modest damage to you, but will change pigs into Zombie Pigmen and supercharge Creepers.

It can't rain in a desert biome, but it might start raining outside the biome if the event triggers.