Do they feed the lobsters in restaurants and grocery stores?

Apparently Not

http://chilipaper.com/FWharf/Lobster/Lobster_FAQ/lobster_faq.htm

Q. How long can lobsters survive when kept in storage without food?

A. Canadian fishing seasons ensure that Nova Scotia lobsters are caught only when the shells are hard and the lobsters are full of meat. These lobsters are in prime condition and could go without food for up to one year at low water temperatures without any change in meat quality or content. A hardshelled, full-meated lobster has energy reserves contained in the hepatopancreas, also known as the digestive gland, or tomalley. A lobster would use these reserves when it is in storage. Lobsters are naturally adapted to going without food for long periods of time. During the winter, when water temperatures are cold (below 39oF or 4oC), lobsters go into a state similar to hibernation and stop feeding. They move about very little, preferring to remain in their rocky or sandy burrows. Clearwater’s Dryland Pound Facilities closely mimics the lobsters’ preferred natural environment, giving them cold (35oF or 1.5oC), clean, salt water and a dark, solitary resting space.

Yeah. They feed them to people.

If they fed them, they would poop in the tank and they would have to clean the tank water more often. They would also have to buy food for the lobsters. It’d be stupid, economically, since the lobsters are fine without food for quite some time, as @wonderingwhy said above.

I don’t eat lobster, or crab: not since I learned how crabs make their living and how lobsters are killed for the pot. As far as I am concerned, those are two species that can live for ever.

Nope. Worked in Red Lobsters, we never fed them. They really don’t last long at all in the tank, in both of the stores that I worked in we generally ran out before the next shipment came in.

The one thing we did do there was to monitor the temperature of the water in order to keep them happy… until they took the final walk to the kitchen.