A good hard-shell lobster can live up to 36 hours out of water if kept cool, moist and refrigerated. Since lobster is a gill breather wet newspaper and/or seaweed helps keep them moist. Since lobsters are seawater creatures never store them in fresh water. If you need to use ice to keep lobsters cold make sure the ice is double bagged. LobsterAnywhere suggests cooking your lobster the day they are received.