The skin on your lips doesn't produce oil. No sweat glands there... Can you recall a time in your life when your lips were oily (like your face can get, some people more than others). The top layer of skin is pretty much dead cells all over.
I would guess that in the case of people who were chronic lip biters, they've developed an enhanced immune response to injury. The lower layers of skin are actually reproducing faster than normal causing a build up of dead cells on top.
Like your body is trying to protect your lips by making a thicker layer of skin, but given the nature of the skin on your lips it doesn't work too well. Like a callus (and those can, now that I think of it turn white in the shower).
It could also be an autoimmune condition similar to psoriasis/eczema which would produce the same effect as above.
There also seems to be a case for nutritional deficiency (and possible viral cause) but these seem to be more the case for people with flaky/peeling lips and no history of biting.