... [the lobster's] nervous system isn't very complex, so it's feeling little to no pain
It references an ABC News article:
... animals with simple nervous systems, like lobsters, snails and worms, do not have the ability to process emotional information and therefore do not experience suffering, say most researchers.
From the Lobster Institute:
... The nervous system of a lobster is very simple – not unlike that of an insect. Neither insects nor lobsters have brains.
For an organism to perceive pain it must have a more complex nervous system. Neurophysiologists tell us that lobsters, like insects, do not process pain.
But PETA disagrees:
Contrary to claims made by seafood sellers, scientists have determined that lobsters, like all animals, can feel pain.
"As an invertebrate zoologist who has studied crustaceans for a number of years, I can tell you the lobster has a rather sophisticated nervous system that, among other things, allows it to sense actions that will cause it harm. … [Lobsters] can, I am sure, sense pain."
—Jaren G. Horsley, Ph.D
Is the neurosphysiology of a lobster complex enough to allow it to feel pain?
(P.S.: I'm consciously not giving a specific definition of pain here, because neither of the above do. But I'm aware that the answer may differ depending on how pain is defined.)