I think it's very hard to say how Reconstruction would turn out under Lincoln.
Lincoln would have insisted black freedman be protected unlike Johnson, but he also would have supported a less harsh policy towards ex-Confederates unlike what the Radical Republicans wanted. And unlike Johnson, he would have had a lot more credibility to pursue a more lenient policy. Lincoln could remove harsh and unpopular military governors and not been opposed like Johnson was.
The issue is whether the freedman would have been better protected in the long term. Obviously there would be a lot of racial animosity still, but I think Lincoln (and the likely future Grant administration) would have maintained Federal protection of freedman even after confederate states were readmitted. It might take another constitutional amendment, but it could be done.
If that happens, then it is possible that a strong Republican Party is built in the south based on those who remained unionists during the war, freed blacks, ex-Whigs who sided with the confederacy, and those who hope to gain patronage under the dominant GOP of the era. If so, then there are competitive elections, and old planter aristocracy will not make a comeback to dominate local politics.
If blacks are kept enfranchised (under Federal protection), it's going to happen. Only if blacks are not kept enfranchised will everything happen as IOTL. Everything depends on the precendents Lincoln will set in first few years.
When Grant's second term is over, the election of 1876 might be very different. If someone like Winfield Scott Hancock wins the Democratic nomination and the general election, then even a Democratic presidency might not rollback established Federal protections of freedman (to be honest, even Tilden or any other nothern Democrat might do so). So we might have 20 years of continuous bipartisan national support of civil rights.
So that is the critical question. Depending on the specifics one thinks will happen, lots of things can become plausible. I think this is one of those time periods where lots of things are in play.