The election of Lincoln, logically speaking, did not require the Confederate states to secede. Nobody, including Lincoln, thought the federal government had the power to abolish slavery where it already existed. As to the territories, Lincoln didn’t have the votes in the Senate to eliminate slavery, the Dred Scott decision precluded him from doing so in any event, and slavery was not economically viable in many of the western states regardless of what the law said.
Secession was thus a rash and unnecessary decision; it was also the only way that slavery could, in the end, be abolished–as a matter of wartime expediency. That is, of course, exactly what happened.
If secession had never occurred, what then? My best guess is that slavery would have been abolished decades later, with compensation paid to the slaveowners; after all, that is what happened in the British Empire. Most of the freed slaves, with few resources of their own to call on and no help from a government that had paid a huge sum to free them, would have ended up as sharecroppers on plantations, with no meaningful political rights.
Does that story sound familiar?