My understanding is that cause and effect create a partial order of events in the universe (and that relatively prevents anything stronger).
My understanding is also that it’s generally useless to talk about “things” in the context of physics. The laws of physics describe events, not objects.
The Big Bang can be seen as the “greatest lower bound” of all events (it must happen before anything else can happen). Similarly the “heath death of the universe” could be seen as the “least upper bound” of all events. No event can happen after it, and all other events must happen before it.
So, the answer would seem to be yes (everything describable by physics forms a lattice).
Has anyone formulated such a notion: the universe is simply the lattice of all events?