Lincoln was much more lenient than Johnson and the Republican Congress in regards to Reconstruction. Had he avoided assassination, Reconstruction would have been over by the 1868 election, with the southern states back in the Union and with former Confederate politicians and military officers governing those states. There is a very strong possibility that Jefferson Davis would have been elected to the US Senate!
Lincoln would have run again in 1868, dumping Johnson off the ticket. Johnson was only chosen to run as VP in '64 because Lincoln needed a Democratic Southerner to balance the ticket. Not so in '68, when Lincoln would replace Johnson with Ulysses Grant, the hero of the Civil War. Doesn't matter who ran against them, with that combination, they would easily have won.
With political reconstruction over in the south, the former Confederates would have to focus on economic reconstruction. The Southern economy had been devastated by the war and the freeing of the slaves, and was in serious need of rebuilding. Rather than return to a purely agriculture-based economy, the few southern urban centers became industrial centers.
Despite what most believe, Lincoln was not a sympathizer with the former slaves, and freed them for purely political and startegic reasons. Lincoln supported deporting all the former slaves to Liberia, but would not have been able to completely implement his plan due to financial constraints. However, had he survived, he would certainly have attempted deportation. The 13th, 14th, and 15th amendments would not have been written, and the blacks would not have gained any temporary political clout. They would have been even worse off than when slaves, for noone would be obligated to support them. By the mid-1880's millions would have die of starvation, disease, and exposure.
Lincoln would probably have declined to run for a fourth term in 1872, being 64 years old and having a mentally ill wife, but would have supported Grant in his bid for the presidency. Of course, Vice President Grant would have won the election with a landslide and set the course for another decade of moderate Republican rule.
After retirement, Lincoln returned to Springfield, IL with his wife and settled in their old home. Not wishing to stay at home long due to Mary Todd's increasing dementia, he would attempt to practice law again, but would most likely settle into a lecturing position at a local college. After Mary Todd's death in 1882, Lincoln, now a widower with only one son still living, would move to Manchester, Vermont to be near his grandchildren.
When Robert ran for President in 1884, Lincoln supported his son by giving campaign speeches and interviews across the nation. Lincoln moved into the White House with Robert's family in March 1885, playing the part of elder statesman. When Robert lost his campaign for re-election, Lincoln returned to Vermont with the family, settling into Robert's Hildene Mansion. As he grew older, Lincoln grew more morose and stopped granting interviews in 1893. His health began to decline as he neared ninety, but his mind remained sharp and alert. In June 1899, at the age of 90, former President Abraham Lincoln passed away after suffering a stroke.