Assuming that Lincoln survives without being seriously wounded, I think that he would continue along the course that he was already following. This course was less punitive toward the south than what many of the Radical Republicans wanted, but it was stronger than what Andrew Johnson ended up advocating. Toward the end of his life Lincoln was supportive of full citizenship rights and the vote for African-Americans - if southern states quickly institute "Jim Crow" type laws and many northern states are reluctant to treat blacks as citizens, he would probably end up supporting the 14th and 15th amendments to prevent the states from disenfranchising part of their population. At the same time, he would generally favor a quick restoration of the southern states into the Union and full citizenship for all former Confederates except perhaps for a few of the most prominent or those who tried to use violence and intimidation against former slaves.
Some of the more radical Republicans are still going to think that Lincoln is too "soft", but I think that impeachment would be more difficult in the case of Lincoln than Johnson. First of all, for all the vilification that he got during the war, Lincoln would have great prestige once the war was concluded successfully. Second, his policies wouldn't be as favorable to former Confederates and unfavorable toward ex-slaves as Johnson's were. Third, in the extremely unlikely event that Lincoln was impeached and convicted on some charge or another, his replacement would be .. Andrew Johnson - hardly what the Radicals would want!
One problem though is that Lincoln might not have lived much longer on his own. He is believed to have had an unusual genetic condition (can't remember what it's called). One of the results of this condition is that a person tends to grow abnormally long limbs, which was indeed true of Lincoln, who is said to have found it very uncomfortable to sit in ordinary chairs and preferred to sprawl out on a couch or even put his long legs up on a desk. Another consequence of this condition, though, is heart weaknesses that often result in cardiac arrest as the person gets older. In other words, Lincoln was probably very lucky to have lived as long as he did, with all of the stress that he did, without having his heart fail. There is a good chance that he would have died of natural causes in the next year or two. Of course, this is not guaranteed.