I can't understand how you would jump over Caesar and strait to his heir. I don't discount Augustus' role in the end of the Republic, but it certainly was his uncle who first crossed the Rubicon and seized power from the Senate. Augustus brilliantly consolidated that power. The Empire flourished, and I'll admit that many of the people did quite well for the most part. However, the perpetual war and ever increasing public spending was a serious burden on her people. In the City, they didn't feel it but many of the provinces did.
Lincoln and Caesar's motives were quite similar. The orthodoxy had become unsustainable and it took a man of will to set things right to save the great nation.
Caesar was a conqueror of his own people, and there's the greatest similarity to Lincoln. The rise of imperial power that they set in motion is the second. I know the analogies aren't perfect but I read in this thread that Lincoln was unique in history and I don't think that's accurate. Caesar is a great example of a Lincoln like figure. They even both died by assassination. (although that's trivial.)