Latest WP instance on Lightsail load balancer gets hammered

I have a WordPress-based website hosted on 2 Lightsail instances (2 GB RAM, 2 vCPUs, 60 GB SSD) behind a Lightsail load balancer. I share a separate Lightsail MySQL database between the two as well as a shared NFS partition for uploaded files.

This should be more than enough to service my site. Every now and then I notice traffic spiking on the 2nd instance added to the load balancer with php-fpm complaining: "server reached pm.max_children setting (30), consider raising it." But it only happens with the 2nd added instance while the first remains fine.

So I added a third instance to the load balancer, and immediately upon passing the health test, the load average on the 2nd instance plummeted to normal and the 3rd instance is now experiencing the problem.

I'm completely at a loss. Any ideas?