As I understand it, restaurants are not supposed to serve local lobster out of season even if it has been frozen, as it just encourages illegal lobstering (though I have seen it served out of season, and a few years ago there was a big squawk when it was served out of season at a government-sponsored banquet). Plenty of other great seafood, though.
There was just a recent thread on the availability of Diet Coke. Someone said stores occasionally run out, but in recent years I have never had any problem finding it in groceries in San Pedro and Belize City.
Dr. Pepper I don't know about as I don't drink it and don't pay attention to it, but it's probably available somewhere.