Lincoln's repetition of pronouns such as "neither," "all," "both," "we", "us," and "each" shows the reader or listener that D) he wants to emphasize that the country's two opposing sides must become one.
The use of pronouns is part of the discourse, as it is any other particular choice of words. The speaker, in this case, is not only addressing the reader and conveying a specific message. He is also getting involved and making both the reader and himself part of the same action, so that every American who was listening could feel the sense of unity Lincoln was trying to spread.