While I'll be the first to concede that the "Gay Lincoln" theory is built around a lot of speculation and circumstantial evidence, the notion that Lincoln was a believer in "God's law" or even particularly religious is without basis in fact. Lincoln is well known to have invoked biblical imagery in his speeches, but virtually all of his intimate friends and family members stated that he did this consciously because he knew it worked politically. Lincoln's best friend William Herndon, his personal body guard Ward Hill Lamon, and his wife Mary Todd Lincoln all conceded after his death that he was not a Christian "in the normal sense," to quote Mary Todd. Herndon stated that Lincoln's religious beliefs fluctuated between outright atheism and a form of very loose and very liberal non-Christian deism. He was probably closer to the latter position around the time of his death, though we cannot know for sure. Stating much more beyond that is simply without basis in history.
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.
If Lincoln's religion was calculated and political then why did he invoke it in private or with individuals when there was not any political gain to be had?