"No sé" and "No lo sé"

I'm not quite understanding the second situation described in this lesson, in which there is a question as to whether "lo" should be used:"Not a response or not immediately after a question

If it is not part of a response or we use it as a response but not immediately after, we need "lo":"

I can see that if there is any preliminary statement in the response before a "No sé" is spoken then the "lo" should be added ("No lo sé"). But what does the phrase "If it is not part of a response" refer to?

Thanks,

John Nolan