Lincoln's assassin, John Wilkes Booth, was a Southern sympathizer as were his co-conspirators. The plan was to assassinate Lincoln, Secretary of State William Seward, and Vice President Andrew Johnson. Booth himself was an actor, and familiar with the theater. Lincoln's visit to the theater had been publicized in the local newspapers. The conspirators had met several times at a Washington boarding house before the end of the war. They hoped to improve the South's situation by means of the assassinations. Only Lincoln was killed, a few days after Lee's surrender at Appomattox. Although Booth and company probably knew of the surrender, they had not yet abandoned the Southern Cause. So it was not a "revenge" killing; but rather an attempt to keep the hopes of the Confederacy alive.
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.