In a LXD cluster HA/Failover/Replication are all properties of LXD itself, not of the containers being run. For example if a particular node gets rebooted or goes down, the cluster as a whole continues to work (e.g. you can list containers, start new containers etc), although operations targeted on containers of the node that went offline won’t work until the node comes back.
There’s no automatic failover for containers, however if you use ceph for your storage pool, then the rootfs image of a container running of a node that goes down will be available on other nodes too, and you can immediately move and restart that container on an online node. This can be scripted as per your own policy.