The word just in just in case is superfluous. Oxford Advanced American defines it. Mind it, it's an idiomatic use.
(just) in case (…) - because of the possibility of something happening
So, you may get rid of that confusion and consider that in case = just in case
Now, the word lest. It is, as described in Oxford Dictoinary, same as in case but if you see the usage, you'll understand in which context it's used and mean in case. When the word lest is used, it gives a bit flair of fear. So, when in case, it's all about fear, lest seems a preferred choice.
Examples from other dictionaries support this -
worried lest she should be late - from MW Dictionary.
She was afraid lest she had revealed too much - from OALD
he was alarmed lest she should find out - from Collins
So to conclude, in case is almost same as just in case and lest is also in case but when you want to include the element of fear. Merriam Webster defines lest as for fear that.
Also, they are interchangeable if in case is just in case and includes an element of fear. Otherwise, they are not always interchanged. I'd prefer saying, "Take these coins as a change, (just) in case you may need." I'm simply giving the change in case that person requires it. He has money and without those coins, he won't get stuck. But for the convenience, I am giving him the change to use in metros and cabs.
On the other hand, I'd use lest when I want to include the fear element. I may say, "she sat up late worrying lest he be murdered on the way home."