It's of course best to cook and eat your lobster immediately, but you can store them overnight in most cases. Unwrap them, they need to breath, and keep in an open container in the coldest part of your refrigerator. Pack with moist (not wet) newspaper. Do not store in contact with ice or tap water and don't let them freeze.
Double bag, cooked, chilled lobsters in freezer bags or vacuum seal. Place in freezer, the colder the better. You can freeze them whole or break off tails and claws. Bodies make great stock! Frozen lobster will keep 3-6 months depending on freezer temperature. Separating the bodies will extend the storage life. Thaw overnight in the refrigerator to use. To cook, steam for 8-10 minutes. Stock made from the lobster bodies makes a delicious base for many dishes.