President Lincoln's night at Ford's Theater is, of course, relevant because that was the night on which he was assassinated. Because the killing happened after the Civil War was over, it did not really have any effect on the war itself.
The relationship between the two is that Lincoln was killed because of his actions during the Civil War. John Wilkes Booth was angry about the ways in which Lincoln had helped to defeat the South in the war. Booth was bitter about the fact that the South had lost and he wanted to take revenge.
So Pres. Lincoln's was killed because of the Civil War, but his death had no impact on that war.