Lobster tails can be frozen after they have been cooked. The Maine Lobster Marketing Collaborative offers instructions for freezing meat still in the shell and meat picked from the shell.
For cooked lobster tail meat still in the shell, first chill the meat for 15 to 20 minutes in a tub of 50 percent ice and 50 percent water. Place the lobster tails in a freezer bag, and cover with cold water. Remove as much air from the bag as possible, and seal the bag. Place the bag in a secondary bag for freezing.
For meat picked from the tail, place meat in a freezer bag and remove as much air as possible. Place the bag in a secondary bag and freeze.