Commonly, deploying multiple Pi-holes would aim for redundancy, not load balancing. (click for more)
You'd only introduce a load balancer if you'd expect that a server would not be able to cope with the number of observed or expected requests.
For the DNS part, even an RPi Zero is able to handle several dozens of clients with tens of thousands of requests a day without breaking a sweat (pihole-FTL has taken good care of that).
But in the event of a failure, you would lose DNS altogether, so I'd understand the desire for a redundant server.
However, as others pointed out already, implementing redundancy by introducing another single point of failure would gain you nothing but a more complicated setup (and maybe a slightly higher power bill).
Most VPNs should allow for configuring more than one DNS server, and deHakkelaar has already explained how DNS itself may alleviate the need for additional redundancy measures.
Still, there might be scenarios where you are not able to distribute two DNS servers.
FritzBox routers e.g. allow only for a single IP to be distributed as local DNS server via DHCP.
If you are facing such a situation, you may want to take a look at solutions using the Common Address Redundancy Protocol (CARP) or the Virtual Router Redundancy Protocol (VRRP).
ucarp and keepalived are among the more well known implementations. They would have to be installed on both Pi-hole machines. Availability would depend on your actual OS (AFAIK, Debian has packages for both).
Personally, I'd prefer CARP over VRRP currently, but I'd only recommend either for solitary Pi-holes:
If you run additional software next to Pi-hole on the same machine, you'd have to evaluate if that software and the clients using it would behave as expected when IPs are switched.
Both protocols do little more than switching an IP from one machine to another, so any software relying on some kind of state (session or not) will fail in that case, unless the respective software itself is prepared to take all necessary steps to run in such a scenario.