Which method of killing the lobster would cause the least pain and distress?
Put the lobster in the freezer for about 30 minutes, it will basically be in a sleeping/coma state when you take it out. Then cut into its head lengthwise to destroy its brain before it wakes up. 

Some people say that killing the lobster in a less stressful way gives the meat a better texture/flavor. But personally I have not been able to tell any difference.

EDIT: Another solution, though not a clean or popular method for lobster; If you destroy its brain faster than the speed pain travels through nerves, it would be dead before the pain reaches the brain. Could be accomplished by shooting it in the brain with a gun... a common method used to humanely kill many things.