…I think would have had a third term forced upon him. And, then, I think, he would have died in office, or shortly after leaving office after his third term.
Mr. Lincoln was not a good eater, never slept much and tended to take too much upon himself. Unlike most men of his day, he never drank alcohol or smoked tobacco, so he would not have died of throat cancer, like Grant, or drunk himself to death like so many politicians of his day.
But I think he would not have lived long away from the great responsibility of the Union, or too long in his sixties (he was 56 when he was murdered), so, if, as I assume here, he had served a third term (illegal, though unstated at the time), he would have left office around his 65th year. It is my opinion he would not have lived long thereafter, even if the various assassins who wanted him dead had failed long term.
And, yes, this speculation fascinates me, as all things about Mr. Lincoln fascinate me, both the things that happened and the things that might have happened, had he lived. It takes no political scientist to know he was thinking beyond the American borders by the time he died. His second inaugural address contained language indicating he wanted to have peace and good relations with all nations (read the end). He had fought off radicals in his own government who wanted war with Britain. He used his friendly relationship with the Queen to prevent war with Britain, which the US surely would have lost, being stretched thin as they were with the Southern rebellion. I think he would have used his relationship with Britain to become the greatest foreign policy President to date. His later utterances had more to do with foreign affairs than others, though he was too consumed with retaining and remaking the Union, out of sheer necessity.
I think he would have had a third term, though no one had ever had one. I do not know who could have beaten him, as long as he wanted to run. And I think he found the task so stimulating, he would not easily have let go, no matter how he protested he wanted to go back to Illinois and practice law.
I think he wanted to be President of these United States of America, clothed with immense power, and thought he was the best one for the job, to boot.