Which method of killing the lobster would cause the least pain and distress? The most common way of killing a lobster is to put it into boiling water, however we can read on Wikipedia page that it is one of the methods which cause pain and distress.

The killing methods most likely to cause pain and distress are:

Placing crustaceans directly into boiling water

Placing crustaceans in slowly heated water to the boiling point

Placing marine crustaceans in fresh water

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Secondly, we can read here about the following study:

Dan Ward, then a grad student at the University of New Hampshire, once hooked an electrode up to a Lobster heart for me and boiled it. The heart beat for 1 minute 53 seconds.

So the question is, what is the most humane way to kill a lobster?
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.