Lincoln admitted the right of secession in 1848, yet no longer supported it once he became POTUS.
Looking at what Lincoln said, he was upholding the right of revolution, not a right of secession under the US Constitution.
"Any people, anywhere. Being inclined and having the power, have the right to rise up and shake off the existing government, and form a new one that suits them better. This is a most valuable, a most sacred right a right which we hope and believe is to liberate the world. Nor is this right confined to cases in which the whole people of an existing government may choose to exercise it. Any portion of such people, that can, may revolutionize, and make their own of so much of the territory as they inhabit."