When it comes to creature horror, this sounds like the slew if bee movies of the 60s/70s. In most cases it was aggressive queen bees attacking a working bee hive so she'd mate with the drones It was nature and an accident.

In the one I remember with a human involved, he ended up being one of the last victims.

In this case, why not an accident? The wrong roaches are bought and put in with the ones already there. Your first victim can be the school lizards, killed as you described. They breed rapidly and get out when some kids decide to take some to play a prank.

There is no knowing where they will attack next and the race is one to find a killing agent as the swarm gets bigger and more are killed...