We can only speculate about what Lincoln's second term might have looked like if he hadn't been assassinated, but there are a few sources we can look to for an idea of what his policies may have been. I'm primarily going to draw from two sources: Lincoln's fourth and final Annual Message to Congress (the precursor to the State of the Union address) from December 1864 and Lincoln's Last Public Address from April 1865, just a few days before his death. Together, these give us some idea what Lincoln's plans were for after the war.

Lincoln's second term would almost certainly have been dominated by questions around how to reintegrate the rebel states into the federal government following the end of the war and what to do about the roughly 4,000,000 newly emancipated black Americans. In 1863, Lincoln had offered his preliminary plan for Reconstruction, which would allow rebel states to resume their relationship to the federal government if (1) 10% of the population of a state took an oath of allegiance to the United States and (2) the state made arrangements to ensure the permanent freedom of those who had been made legally free by the Emancipation Proclamation. In his Last Public Address, Lincoln suggested that this was not the only plan for Reconstruction that he would accept, and indeed the plan that the Republican-controlled Congress eventually adopted after Lincoln's death was far more stringent that the one Lincoln had proposed. However, he did make it clear in his Annual Message to Congress that he would not accept any plan that did not secure the permanent freedom of the formerly enslaved, saying:

"I repeat the declaration made a year a ago, that "while I remain in my present position I shall not attempt to retract or modify the emancipation proclamation, nor shall I return to slavery any person who is free by the terms of that proclamation or by any of the acts of Congress." If the people should, by whatever mode or means, make it an Executive duty to reenslave such persons, another, and not I, must be their instrument to perform it."

Would Lincoln have supported Congressional Reconstruction? Would Congress have gone along with Lincoln's proposal? Or would Lincoln have developed some alternative plan for Reconstruction along with Congress? There's no way to know for sure, but Lincoln clearly favored the rapid reintroduction of rebel states in order to "again get them into that proper practical relation" with the federal government.

In his Last Public Address shortly before his death, Lincoln also spoke about his desire to extend voting rights to black Americans, though he limited his support in this address to "the very intelligent, and those who serve our cause as soldiers." Though a lukewarm endorsement of black voting rights by any modern reckoning, even this was seen by some as a radical step towards racial equality. It seems likely that Lincoln would have supported measures like the Civil Right Act of 1866, which established that black Americans were citizens of the United States, and the 14th Amendment, which promised equal protection under the law. Lincoln's successor, President Andrew Johnson, opposed both of these measures, though each became law despite his opposition.

Aside from the questions of Reconstruction, Lincoln likely would have continued to encourage settlement of the American West, as well as the necessary infrastructure to make this happen. As President, he strongly encouraged westward expansion through his support of legislation like the Homestead Act of 1862, and in his message to Congress he discusses the "great enterprise of connecting the Atlantic with the Pacific States by railways and telegraph lines". The Transcontinental Railroad was chartered by the Pacific Railroad Act of 1862 during Lincoln's first term, and was eventually completed in 1869.

Lincoln also saw a role for the United States on the world stage. In his 1864 Annual Message to Congress, he supported, among other things, U.S. support for Liberia to help that nation combat the slave trade in Africa, the creation of an intercontinental telegraph line connecting the U.S. to Europe via the Bering Strait (a project which was ultimately abandoned in 1867), and the "encouragement of immigration" to the United States, calling immigrants "one of the principal replenishing streams which are appointed by Providence to repair the ravages of internal war and its wastes of national strength and health". All of this is to say that, even while focused on the most severe domestic crisis in American history, Lincoln continued to look outward and work towards ensuring America's place in the international community.

So, while we don't know what Lincoln's second term would have looked like, we can make some educated guesses. We know that Reconstruction would dominate the next twelve years after his death, continuing under both of Lincoln's presidential successors - Andrew Johnson and Ulysses S Grant - and it is almost certain that these same issues would have dominated Lincoln's second term. Based on Lincoln's own words, I think it's fair to say that he would have prioritized the reintroduction of rebel states to ensure representation for all states at the federal level, advocated for and defended civil rights for black Americans (likely including the right to vote), continued to push an ambitious plan of national infrastructure and westward expansion, and further developed America's role on the international stage.