In this sentence: Vienes conmigo al cine? -________. Estoy cansada.
Why are both "no se" and "no lo se"correct, if it is expressing doubt?
In this case, because it is a response immediately after a direct question, we can use both. It is actually expressing doubt, as in "not sure if I want to go or not", so that could have confused you, I can see. I have re-worded this part in the lesson so it is more clear, so it is now stating that even when it is expressing doubt, the "no sé" as the only option, happens when it is not an answer to a direct question. Otherwise you can use both.
I hope this helps,
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