What gave Lincoln that perceived authority was the attack on fort Sumner, we are nto talking about attacking anything, we are talking about a vote of the people to secede from the Union in accordance with our existing Constitution.
Unless your actions are legal under the U.S. Constitution then it doesn't matter what your constitution says. And under the Constitution you just can't walk out.
"All the obligations of perpetual union, and all the guaranties of republican government in the Union, attached at once to the State. The act which consummated her admission into the Union was something more than a compact; it was the incorporation of a new member into the political body. And it was final. The union between Texas and the other States was as complete, as perpetual, and as indissoluble as the union between the original States. There was no place for reconsideration or revocation, except through revolution or through consent of the States." - Texas v White, 1868