Explain, if Lincoln had not been assassinated, would he have pushed for equal civil and political rights for black people?
It is, of course, impossible for us to know what Abraham Lincoln would have done had he lived. The evidence is contradictory and it is impossible to know how Lincoln would have interpreted the best interests of the United States.
It is possible to argue that Lincoln would have pushed for African American rights. This was, after all, the man who had pushed to end slavery. He had issued the Emancipation Proclamation, making the Civil War into a war that was fundamentally about slavery. He had pushed hard for the ratification of the 13th Amendment as he ran for reelection in 1864. This shows that he had at least some interest in the rights of African Americans.
On the other hand, Lincoln did not explicitly push for civil or political rights beyond emancipation. Lincoln is known to have said before the war that he did not think that African Americans and white Americans could ever really live together as equals. As the war was winding down, Lincoln’s “10 Percent Plan” did not require Southern states to give African Americans any particular rights. He also pocket vetoed the more demanding Wade-Davis Bill (though we should note that it did not call for black rights either), preferring to let the Southern states back into the Union as soon as possible.
Therefore, we are really left to guess. There is evidence for both sides and no way to know for sure.