I would argue that Lincoln did this because he was trying to be conciliatory. He was already looking forward to a time when the war would end and the United States wouild be a single country once again.
President Lincoln's main goal in fighting the Civil War was to preserve the Union. He believed that it was that important to keep the United States together. In the Gettysburg Address, Lincoln was trying to promote this agenda. If he had referred to the separate armies and if he had referred to slavery, he would have been talking about the things that divided the country. Instead, he wanted to talk about the common heritage and common ideals held by all Americans. This is why he did not mention the separate armies and did not mention slavery during this speech.