BTW, while it looks like you've shown it to be traditional load balancing,
I ought to explain that this is also not a very good idea. The
loadbalancer is a single point of failure, usually. Loadbalancers are a
good idea for stateful, high-work-request servers such as web servers
running web-apps. This allows you to apply many servers to what then
appears to be a single service. This is well worth the expense of a single
point-of-failure, since what you really wanted was a single, bigger and
exponentially more expensive server. The multiple small cheap servers
with the load balancer give you that view. When the load balancer detects
failure and drops that failed server, the loadbalancer isn't really
offering "higher availability" than a single server, but is rather
compensating for the fact that multiple small cheap servers will
collectively crash more frequently.
However, DNS service is comparatively low-work-request, and low latency.
Generally, people are seeking high availability and load distribution for
DNS caches. But the work of the traditional load balancer is probably
comparable to the work of the DNS server. So the benefits of multiple DNS
servers behind a single load balancer are probably negligible.