That is the most grotesque lie of all. The union was a voluntary compact, states couldd leave at any time, and many states (including northern ones) used the threat of secession as a trump card against consolidation of federal power. The notion that secession was illegal is pure revisionism.
Of course after the war the feds made it illegal, but that's beside the point.
It isn't a lie. There were differing opinions but the understanding that prevailed several times before during and after the war was the states had no unilateral right to leave the union, never even existed as states before the union was created and resolved to form a more perfect union amongst themselves.
I think its pretty clear that any state wanting to secede would have to get 2/3 of the states to agree to modify the Constitution to allow it becasue there's no part of the present Constitution that allows a state to leave the Union.