But if we accept your premise that the southern states had left the union, as you say was their right, then there was no more compact for Lincoln to break. You can't renounce your place in the union and under the Constiution then complain that they no longer protected you.
Instead he chose an unlawful war and relentless and abominable invasion to force the south to submission.
It was the act of a tyrant, a truth he and his accomplices ignored, all in the name of forcing by armed aggression the unlawful restoration of the Union, a right no just government would claim to possess or such action undertake.
They claimed a higher purpose, yet broke the compact and the law to achieve it. They were no longer a nation of laws, but no more than a mob, hellbent on vengeance and destruction.
They achieved their purpose and then proceeded to create court rulings(White v. Texas) and concoct other peculiarities in an attempt to justify their crimes. They inflicted Reconstruction on a wounded and weakened south to cause yet more pain and suffering.
Their desire for domination was insatiable and they instituted the arrogance and brute force of statism that has marched it's way through the years since and right into today's reality.