Regarding Lebanon-for all of Lebanon’s woes, it still survives, it hasn’t broken up into a new civil war; and for all the criticism of its political system, maybe its unique political system has been one of the factors preventing that outcome. And I think Lebanon’s biggest problem is that the national government lacks a monopoly on force, with sectarian political parties controlling their own militias beyond state control (of which Hezbollah’s is the most significant example.) I don’t think the “cantonalisation” proposal for Israel is going to lead to that, since all the versions of it I’ve seen have the military, intelligence, law enforcement, prisons, etc under the 100% control of the national government. Lebanon’s problem in that area is a leftover of its civil war; Israel is not going to have the same problem unless it has a civil war (which I still think is very unlikely)
I'm not doubting it will be grounded in peace, a stalemate can be a form of that as nothing will happen. A state not only keep residents safe (ideally they should try do this). It becomes a failed state when a state is no longer in control. When other government services like utilities are no longer delivered, that's when the failed state question can also come into being. Lebanon isn't quite there thank goodness but it's not great either.