Had Lincoln agreed to negotiate the terms of the dissolution of the Union, he would have violated the terms of the oath he had just taken “to the best of my Ability, preserve, protect and defend the Constitution of the United States.”
Nothing in there about the President being authorized to negotiate the breakup of the Union established by the Constitution.
There were several possible constitutional possibilities that would allow for secession, including an amendment and a lawsuit in the Supreme Court. The seceding states chose to take none of them. They rested their claim, of their own free will, on “an appeal to arms.”
When you appeal to arms, you really should take into consideration the possibility your appeal will be rejected.
There is nothing in the USC against it either.