"Ajouter un tiers de lait et battre le mélange."
yes because not knowing where the milk comes from (a liter, a half liter ?), the recipe writer would rather refer to a third of the preparation container which was probably defined before.
if it were "un tiers DU lait", it would mean that the exact measure needed for the entire recipe was already defined at the beginning of the recipe (on the list of ingredients).
but to be frank with you, I would rather read the entire recipe to really understand what is meant by "one third (of what?)"