Lincoln would not, most likely, have done much to interfere with segregation in the South. For one thing, segregation was something he supported in his own State of Illinois, where he supported black exclusion laws and the like. There is no evidence he felt it was a bad policy.
And
Lincoln's Reconstruction Plan was even more lenient than
the one adopted by his successor, Andrew Johnson. Johnson at least tried to break the power of the planter aristocracy in the South. Lincoln's plan did nothing like that, and seemed to be aimed at restoring the South to the Union with as little change to Southern society as possible...with the exception of the abolition of slavery, which he did insist on.
That being said, in a South where Reconstruction had proceeded according to Lincoln's plan, segregation might never have arisen at all. The Jim Crow laws of the 1880s and onwards were largely a reaction to what had happened in the South during Radical Reconstruction...namely the use of the black vote, coupled with massive disenfranchisement of Southern whites, in order to establish Republican control of Southern State governments. This would not have happened under Lincoln's Reconstruction Plan. Lincoln never talked about giving freedmen, en masse, the right to vote, nor of organizing them as a Republican voting bloc to put Republican governments in power in the South. He did talk about giving those blacks who had served in the Union armies the right to vote. And he talked about re-enfranchisng almost all of the former Confederates, with the exception of some high-ranking political and military leaders. In that situation, blacks would have been a relatively small bloc of voters in each State and would not have been able to be used to control the State governments. And if that did not occur, the Jim Crow laws probably would never have been passed, either.
This is not to say that everything would have been rosy for blacks even if there was no de jure segregation under Jim Crow. The legal repression of blacks might well have still existed, only in a different form. It just wouldn't have been via segregation.