Question: how to beat zvp lategame?
Answer: Get the Swarm Host count quickly up to 10 or more, then you can either use a Nydus Worm through the Overlords you put out in the map, or if you have decent creep spread just move the Swarm Hosts out. Send your Swarm Hosts either to the Protoss 3rd or Natural, and attack the Nexus only, with your Locusts.