Lincoln was assassinated because the Confederacy lost.
The earlier compromises meant that the US Congress had a delicate balance between slave-owning states and free states. As a result of the Mexican-American War, the USA will now have many new states to be added. If many new states became slave-owning states, that will permanently change the balance of power. If many new states became free states, that will permanently change the balance of power. With such high stakes, "Bleeding Kansas" will be repeated over and over again. When a newly incorporated state holds elections to determine free/slave, armed mobs of outside agitators will move in and perform street fighting. The "Fugitive Slave Laws" meant that if you were a sheriff in e.g., New York and believed that slavery was immoral, the law legally compelled you to aid slave hunters to hunt "fugitive" slaves. In reality, anyone who was not white could be chased down and captured, even if they were not slaves or recently emancipated. This happened in the northern free states. The South argued that they were fighting for states' rights and their southern heritage and way of life. It just happened that their way of life was entirely built on the backs and suffering of slaves.
Yes, the history of the USA would have been very different if Lincoln hadn't been assassinated.
Johnson, who succeeded Lincoln, was a southerner from a poor background who desperately wanted the social approval of the (former) slave owning upper class. He was considerably more lenient than almost anyone else would have been in forgiving them for rebellion and restoring their citizenship rights. He stopped the attempts to redistribute land to the freed slaves, which led to decades of almost-as-bad-as-slavery conditions for blacks forced into sharecropping.
Personally, I suspect if Lincoln hadn't been assassinated, the USA would have written an entirely new constitution to fix the systemic issues that led to the war, rather than a poor attempt to paper over them with a few amendments.