I can recommend three restaurants in Charlottetown that serve very good lobster.
For a traditional lobster supper - served hot or cold - go to the Water-Prince Corner Shop. This is a popular place with visitors and locals. It doesn't look like much on the outside but their food is very good. Reservations vital!
The Claddagh Oyster House is a great spot specializing in seafood. 'Upstairs' houses an Irish pub. You can't go wrong. Reservations recommended.
Finally, The Brickhouse. This spot doesn't specialize in seafood but what they do they do very well. In particular I recommend their short surf which is braised beef short rib with lobster tail on top, served on a bed of delicious local veggies. Reservations recommended.
Hope you enjoy your visit to our beautiful Island!