Welcome to the forum jbonez

There is no build in functionality to persist the script state.
I see some previous discussion . I recall more discussion but have not found it yet, perhaps I was thinking of downgraded's experimental .
I am not sure if anyone has tried to port Pluto or other Lua extension attempting to implement such a feature. Even if the script state by itself were serialized, interdependence between native and managed code could be challenging. It might end up simpler to store entity and system state explicitly and restart the game with that. (Such an implementation might help with networking and replays.)