No sé and no lo sé

Hola Shirley

When we say "If it is not part of a response" we mean that there hasn't been a question before so you find that "no lo sé" inside a statement that someone makes. This is an example showing this:

Yo debería saber dónde trabaja mi hija, pero no lo sé. I should know where my daughter works, but I don't know.
So this has been said by someone who hasn't been prompted by any previous question. 
In this other example, we can see that the "no lo sé" bit is part of a response to a question, but not immediately after (there is some extra info before), so, you use "lo" here too. 
-¿Cómo se escribe esa palabra? -Pues voy a mirarla en el diccionario porque no lo sé.-How do you spell that word? -I 'll look it up in the dictionary because I don't know.