We're talking about Lincoln's quote and the asinine attempt that Lost Causer's always try to make it sound like Lincoln was supporting unilateral secession. He wasn't. He was recognizing that the right to rebellion in an inherent right in all people. And that they do have the right to rise up and rebel if they feel the circumstances warrant. But Lincoln is not saying or implying that such actions were legal. Or that they were guaranteed success. The key, as Lincoln said, was 'having the power'. The South did not have that power, and the obvious reason was that their cause was not important enough to do what it took to win.
To the Goon then, secession is by default implied legal, as the Constitution was/is (still) totally silent on the subject.
Nothing in the Constitution forbids secession. But since you brought up the concept of implied powers, then clearly implied in the Constitution is the need to gain the permission of the other states to leave.