For best quality, lobster should be frozen uncooked. Freeze the lobster whole, or clean it and freeze just shell portions that contain the edible meat. (Some lobsters have large front claws that contain edible meat, while others have edible meat mainly in the tail section.)
Freeze lobster in the shell to help keep the meat from drying out. Simply wrap the whole lobster or lobster portions in moisture-vapor resistant wrapping and freeze. Lobster can be cooked and then frozen, but the quality will not be as good.
This document was extracted from "So Easy to Preserve", 5th ed. 2006. Bulletin 989, Cooperative Extension Service, The University of Georgia, Athens. Revised by Elizabeth L. Andress. Ph.D. and Judy A. Harrison, Ph.D., Extension Foods Specialists.