This election would result in President Lincoln II continuing in office for another four years.
I cannot see much change in the electoral map, except possibly Missouri goes to Parker. Lincoln would not have been quite as strong a nominee as Roosevelt. However, the Republicans practically owned the Presidency in this era and Lincoln would have been a credible nominee. Roosevelt would have been a good VP pick and would have gone over well. The Democrats, of course, continue their domination of the deep south, but fail to break of out that area with very few exceptions. In 1904, the voters really had no compelling reason to turn out the Republicans, and they would not have turned out President Robert Todd Lincoln.
The fact his name was Lincoln and the fact he was the President going into the election in a favorable time for the incumbent party and administration would only help his cause.
Lincoln/Roosevelt 317
Parker/Davis 159