Lee at Appomattox Courthouse finds himself essentially backed into a corner in every possible sense of the word. Richmond, the capital, has been abandoned. In the far western theater, the Union holds Vicksburg and can move up and down the Mississippi at will. His troops are ragged, demoralized, and out of supply, coming off a broken siege at Petersburg which in a way represented the last major engagement of the eastern theater. Lee's plan at this point is basically desperation: move west, link up with General Johnston's Army of Tennessee (and hope for supplies), and try and drag the fight out a bit longer. This hinges upon the belief that all that lies between Lee and clear ground is a Union scouting force of cavalry. When he makes the initial probing attack, Lee quickly discovers this is not the case. Sizing up his forces, he quickly realizes that any attack is going to be suicidal; dispersing the Army of Northern Virginia, if ever considered, would have been unfeasible. Assuming they get through the Union lines, it's unlikely they'll be able to regroup coherently and complete the planned link-up. In short, Lee surrendered because he had no honorable options left to him.