Cooked lobster can be frozen, but the quality of the meat is diminished. Freeze uncooked lobster in its shell to preserve the taste of the meat and to prevent the meat from drying out.
Store live lobster in an open container in the refrigerator. Keep it moist using wet seaweed or paper towels dampened with seawater. Newspaper dampened in seawater can also be used to keep the lobster's gills moist. Lobsters can live up to 48 hours after purchase or capture in this environment. After the lobster is cooked, place any unused or uneaten portions inside airtight containers in the refrigerator for up to three days.