It is unknown how Abraham Lincoln is still alive, but he is the 16th president of the United States, and is still President in The Grim Adventures of Billy & Mandy and in Evil Con Carne.
He is a friend of Mindy in "Educating Grim", but it is unknown if they still contact each other, however it's highly unlikely as Mindy only befriended him in an attempt to make Mandy jealous. He also build a log cabin while being shirtless.
In Evil Con Carne, on top of being president, he directly commands SPORK and Cod Commando.
In Underfist Mandy is elected the new President, and thus it is assumed his term ended.