Min heap problem: merge k sorted lists into one sorted list in O(n lg k) time

Recall this problem -- define an algorithm that will merge k sorted lists into one sorted lists in O(n lg k) time where n is the number of elements in ALL the input lists...

My question is why do we define a comparison that states the following:

"We shall also need to define comparison with empty lists, and so we define it taking that any non-empty list is smaller than the empty list."

when we already established this:

"Now let us take our k sorted lists (of arbitrary lengths) and define the comparison between the lists by their smallest elements."