While mammal embryos are developing, they have a "tube" down their backs called the neural tube. A stripe along this tube is called the neural crest, and all neurons (nerve cells) start out in the neural crest. Pigment (color) cells are a special kind of neuron.
Normally, at certain points in their development, embryos make various proteins that act as signals to the neural crest to release the neurons, which then travel across the body and fill it with nerves and pigment cells. If the genes for any of these proteins are changed, though, the protein won't work. Different broken proteins cause different problems, but basically, some types of neurons don't leave the neural crest and spread throughout the body. In guinea pigs these include pigment cells and the nerves that make up the back of the eye, and possibly sometimes nerves in the digestive system that stimulate the muscles to keep it moving.
After doing a lot of reading, I think the protein that's broken in lethal white guinea pigs is called MITF (microphthalmia-inducing transcription factor). MITF is associated with similar disorders in hamsters and mice, causing white hair, small or missing eyes, and skeletal deformities including tooth problems. MITF is also associated with other processes in the body, like bone formation and growth, and deformed MITF can screw with that process, resulting in the teeth deformities most lethals have.
Deafness in lethals may be a result of neurons never getting to the inner ear, or it could be related to the lack of pigment. If the inner ear has no pigment cells, the nerve cells related to hearing can die off. This is seen in other animals, such as cats, where white cats can be deaf. Dalmatian dogs with white ears are much more likely to be deaf than ones with spotted or patchy ears.
A single deformed copy of the MITF gene causes roan or dalmatian markings in pigs. The protein-making process works on both copies of the gene, so the pieces of MITF floating around are half good and half bad. The good ones trigger normal neuron movement from the neural crest, but there's only half as much of it as in a pig with two good copies of the gene. So about half as many pigment cells get out in time to make it all over the body. Therefore, the white hairs of roans and dals are, like the white hairs of lethals, not attached to pigment cells. The white hairs of other pigs are attached to pigment cells that don't make any pigment for other reasons. Since the two openings in the neural tube are in the head and butt, pigment cells that got a late start or didn't get very far cluster in the head and butt, making them solid colored instead of roaned. (This also helps roans to be able to see and hear.)
A roan with solid-colored head and butt:
For more info on neuron migration from the neural crest, try
this site. It focuses on rats, who have a different "lethal white" gene and therefore different symptoms, but the process shown is the same. Plus, it has pictures!