Deja vu? We had the exact same question just a few weeks ago!
Alexander is right. You need to find a way to keep the water super cold. Chillers will do this, but they are really expensive (even the smallest ones are usually $400+). And I don't know if reef tank chillers will even keep water cold enough to keep a lobster. People that have done this apparently have to use an industrial strength chiller, like the ones they have in seafood restaurants and supermarkets.