Slate has an article by Brook Thomas, pointing out that there were no government-printed ballots in the United States before 1888. Thomas feels the need to write this because Law Professor Akhil Reed Amar had an op-ed in the New York Times of February 7 that says, “Lincoln was not on the ballot in some states in 1860”. Amar also made that error in his U.S. Supreme Court amicus in the Colorado Trump ballot access case.
Lincoln didn’t receive any votes in most southern states in 1860 because no one organized a slate of Republican presidential elector candidates in those states and printed up ballots bearing their names. Probably individuals who might otherwise have identified themselves as Republican presidential elector candidates were intimidated from doing that. Also because voting was not secret in those days, those tickets, if they had been prepared and distributed, would have received very few votes.
Here is the Thomas article, which has a link to the Amar piece.
Slate states in which Lincoln did have presidential elector candidates were Delaware, Kentucky, Maryland, Missouri, and Virginia.