That's easy. Lincoln would have done just what the Republican platform called for.
Regarding slavery they promised to stop it's expansion into territories which didn't want it.
Otherwise, they would have done nothing to roll back slavery in States where it was already legal.
I expect they would also take steps to reduce the affects of the SCOTUS Dred Scott decision.
In short, Lincoln would have been the first openly anti-slavery President, but could have & would have done nothing to outlaw slavery in the South.
Regardless, it was anti-slavery enough to drive Deep South Fire Eaters to declare first secession, then Confederacy and war on the United States.
I would think the Republicans would also have repealed the Fugitive Slave Act, which would have caused the South to secede anyway.