LAN connection on separate itineraries?
 

How risky would it be to buy a CUZ-LIM flight that arrives in LIM around noon when I'm scheduled to depart on a LIM-JFK flight that leaves around midnight the same day?

Both flights would be on LAN, but they would be on separate tickets (award flights CUZ-LIM, revenue ticket LIM-JFK). I'm concerned that if CUZ-LIM is canceled, LAN is only obligated to get me to LIM on its next available flight, regardless of whether that would mean that I'd miss the JFK departure.

If that happened, do you think LAN get me all the way to JFK or take me as far as LIM?

This is about as un-risky a connection on separate tickets that you can have. In fact, show both tickets to the agent @ CUZ and your bags will probably be checked through to JFK. There are also 5 CUZ/LIM after noon on LP.