F5 Load balancer LVM Monitoring scenario - assistance

The sync between the active and the standby is just to sync any changes in configuration between the active and the standby unit. If it shows "disconnected" it can be a couple of reasons and would be independent of the active unit being unavailable. The sync should be configured to use a different network than the fail over network. When there's an issue with the active unit - the F5 will issue a communications error alert via SNMP to whatever SNMP IP's you have configured. I'd be less concerned with the sync in a failover scenario - though if your F5 isn't set to auto sync, there is always a chance in a failover situation the standby unit won't have the right running config.