If Lincoln had acknowledged the right to secede, the war might not have happened at all.
If Jefferson Davis had not ordered Fort Sumter to be fired on the war might not have happened at all.
There is and never has been a “right to secede”. It is mentioned nowhere in the United States Constitution. Lincoln could never abolish what never existed. The nearest any of the Founding Fathers got to enumerating any such process (why should they waste time on destroying the union they fought so hard to create?) was the suggest that leaving be conducted in the same method as states entered: consent of the states.
The war might never have happened had the southern states stuck to the spirit, if not the letter of the constitution.