How does soaking liver in milk work?
My knowledge about the phenomenon itself is limited but I did see it mentioned in "Modernist Cuisine" (Nathan Myhrvold, p. 147)


  Many recipes for foie gras, liver, sweetbreads, and other offal include a soaking step before cooking. For kidneys, 
  this step serves a very simple purpose: to remove any trace of the animal's bodily fluids. Recipes often call for 
  soaking foie gras, liver, and sweetbreads in milk. It is often said that milk improves the taste, purges blood, lightens 
  the color, or affects some other property of the meat. We were skeptical, so we tried several experiments. With 
  a mild-flavored organ meat like foie gras, we could taste a difference, but, frankly, in our tests, we prefer the taste 
  of water-soaked to milk-soaked foie gras. With stronger-flavored organ meats, there is even less of a difference than 
  with foie gras. So our suggestion is to simply soak the meat in water. 


So, there you have it.