The OSMF Nominatim servers used to be set up as a cluster for a while with one master server and the others being replication clients. The advantage of this setup is that you are guaranteed to get consistent responses from the servers and the servers running as replication clients can get away with less powerful hardware. The disadvantage is that the setup adds quite a bit of overhead for system administration.
Nowadays, we just run parallel independent installations on the servers. It’s just easier to maintain. You will get slightly different responses. In particular, the place_id, the unique ID assigned to each object, will be different on the two machines. Most users will never notice any difference. Still, it will be a good idea to configure your load balancer in a way that the same user usually ends up at the same machine.