And upon this act, sincerely believed to be an act of justice, warranted by the Constitution, upon military necessity, I invoke the considerate judgment of mankind and the gracious favor of Almighty God.
Well, Lincoln told Orrestes Brownson at the time that his purpose was to gain a political advantage at home and in europe for his side in the war.
The section you quote, BTW, was added at the advice of the cabinet, which did include some Christians. Lincoln was not planning to put it in the original.