It's commendable that people do not want to inflict pain on animals, but this one is definitely false on the first account (screaming) and probably false on the second (pain).
Lobsters Cannot Scream
As for the "scream," think about it. Lobsters have no throat, no vocal cords, no lungs, so how could they scream at all? The fact is that the noise is caused by air trapped in the shell. When heated it expands and forces itself out through small gaps, causing the sound - sort of like when you force air out between your tightly clenched lips to make a rude sound. A lobster can no more scream than a snail can walk or a jellyfish can play the piano.
Do Lobsters Feel Pain?
What about pain? No one can know for sure what a lobster or similar critter feels, but we can make educated guesses based on what we know about pain in other animals, specifically humans. And I am talking specifically about pain, not discomfort or unpleasantness. Pain doesn't just happen automatically—it is the result of specific receptors, nerve pathways, and brain regions all cooperating to convert certain physical stimuli into the perception of pain. This has all been pretty thoroughly worked out in humans and other vertebrates. However, lobsters and other crustaceans are not vertebrates and simply do not have these nerve pathways and brain regions (they don't have a real brain at all, for that matter). To claim that lobsters feel pain in the same way we do is a real stretch unsupported by solid evidence.
Best Practices for Cooking Live Lobster
While it is not likely that lobsters feel pain in the way we do, it seems best to play it safe and minimize any discomfort they may feel. Partial freezing is the best method for this. Place the live lobster in the freezer for 15 to 30 minutes, depending on size. This anesthetizes the lobster without freezing the meat. Then put it immediately in the pot of boiling water, which kills it instantly. Some chefs go a step further and "spike" the lobster by using a sharp knife to sever the lobster's nerve cord just after freezing and before putting in the pot. There are details on these techniques in the references below.
