My question is: when does one use 'juste' in front of 'au cas où' and when is 'au cas où' used by itself?

From the lesson on 'au cas où ' It is optional... adding the just or not. It is very similar to how it is used in English.. for emphasis. maybe to add more need for preparedness to the probable circumstance .

Yes, Jameson is correct: adding "juste" is optional. It is also optional in English either to say "in case" or "just in case".

Use of 'just' is not opTional in EnglisH. 'In case'needs a subject. so, 'In case you need some tea, there's a pot..' etc is fine. But ' I'm going to see her, in case.' begs the question, in case of what. So you need just. 'I'm going to see her, just in case.'