It and will not allow you to detect when one member of the LAGG goes down
Well you could look for traps from the switch/stack doing the LACP for LACP issues but it really seems like overkill but it depends on the application.
Everything always comes down to the endpoints. Unless you are going to LACP to two NICs in every endpoint to two different switches (You can LACP a group across stack members or sometimes with multi-chassis trunking), when the switch that the endpoints are connected to has a problem, those endpoints lose connectivity.
On all of your LANs:
X.X.X.1 CARP
X.X.X.2 Master interface
X.X.X.3 Backup interface
All clients pointed to .1 for routing, DNS, etc.