Abraham Lincoln faces a different direction on the penny because the penny is an adaptation of a plaque by Victor David Brenner. The illustration was placed on the penny as a result of President Theodore Roosevelt's love for Brenner's work. Roosevelt recommended to have the illustration placed on the penny during Lincoln's centennial year of 1909.
The penny differs from the nickel, dime and quarter in two distinct ways: First, Lincoln faces to the right on the penny, while the presidents depicted on the other coins face right. Second, the penny is a different color and comprised of copper. Both of these differences are a result of Brenner's plaque.
The portrait of Lincoln on the penny is a replica of Brenner's plaque; however, Brenner's plaque is actually a replica in its own right. Brenner's plaque is based off a photograph of Lincoln from 1864. Lincoln is facing left in the photograph, so naturally Lincoln is also facing left in the plaque. Therefore, Lincoln is facing left in all three works: the photograph, the plaque and the penny.
The penny's dark coloring comes from the fact that the plaque was made of bronze. To maintain a similar color, the U.S. Government circulated the penny with a copper coating.