What do we know about what Lincoln would have done with reconstruction if he hadn’t been killed?
All we know is what Lincoln did while he was alive, and what he said and wrote about what he might have done in the future.
In four states, the process of Reconstruction began while Lincoln was still alive. The four states were Virginia, Louisiana, Arkansas, and Tennessee. In each case, Lincoln insisted on the abolition of slavery, but did not insist on African American suffrage. His plan allowed former Confederate supporters to vote if they took an oath of future loyalty. Lincoln also supported creation of the federal Freedmen’s Bureau, an agency designed to assist former slaves with education and with getting started as small farmers, but stopped short of endorsing large-scale land redistribution.
Lincoln had to work against ongoing Civil War, and war aims were never far from his mind. He wanted his new regimes to be as moderate as possible, and attract support from Southern whites, in order to weaken the Confederacy.
Above all, Lincoln wanted to remain flexible. He vetoed the Wade-Davis bill in 1864 because he didn’t want to be “inflexibly committed to a single plan of Reconstruction”. And indeed, reality had a way of intruding. After the Civil War ended and die-hard Confederates resumed participation in Southern elections, the state governments they elected veered sharply to the right—more pro-slavery, more anti-black, more anti-Northern. Had he lived, Lincoln would have had to adjust to the new “reality on the ground”, and would probably have moved closer to the so-called “radical Republicans” in Congress.