I wonder if Lincoln would have been the first president to win three terms or at least the first one to try it... in OTL Grant seriously considered it and wanted it, Teddy Roosevelt tried it, and FDR did it. Perhaps, given how great an orator and debater he was, he could say "Reconstruction isn't over, I don't want to see that all those lives were lost in vain" Almost certainly I think Johnson would not go on to be elected on his own in 1868 unless he ran as a Democrat and Lincoln split the Republican party. If Lincoln did TRY or people THOUGHT he might run for a third term that would probably solidify in the South the idea of Lincoln as a tyrant. Lincoln almost assuredly is assassinated sooner or later in that case.
I admit almost certainly Lincoln wouldn't want a third term, but as an ex-president starting in 1869 he'd be involved in some manner in promoting equal rights and a fair southern electorate. Right? Some sort of Global Lincoln Initiative?