When left at temperatures of 40 degrees Fahrenheit or more, cooked lobster only stays fresh for about 2 hours. At temperatures of 90 degrees Fahrenheit or higher, cooked lobster only keeps for 1 hour. Cooked lobster stays fresh up to four days when refrigerated under 40 degrees Fahrenheit.
Cooked lobster can be frozen for up to 6 months before the taste and texture begin to change and the lobster is no longer fresh. Cooked lobster should be wrapped up tightly in aluminum foil before being stored in the refrigerator. In the freezer, cooked lobster should be stored in foil, a freezer bag, a freezer container or a freezer wrap.