This has sort of been the holy grail of lobster fisherman forever. The trouble is that another lobster is among a lobster's favorite foods.
Some guys do store their lobsters in giant "cars" while they wait for prices to rise, and don't suffer enough losses to make it not worthwhile.
The bigger trouble is that a lobster is about 7 years old before it is big enough to catch and eat legally. I imagine the cost of raising one would easily outstrip the payoff. I suppose if there were a massive farming industry you could lower the legal size, but would a lobster that small be worth eating? Maybe you could modify them genetically to moult more often, like a shrimp.