Lincoln was taken to England, and eventually went into exile there. He swore the oath and became a full British citizen in 1870, entered politics and was elected Member of Parliament for the
University of London in 1880 as a Liberal. He would eventually rise high in British politics*.
This was one of many events that ensured a wide gulf between the newly independent Confederacy and the British Empire in the years after their War of Independence.
* Lincoln's parents were citizens of His Majesty's Commonwealth of Virginia, thus were citizens of the Empire, which extended to their children (but not grandchildren). Via this torturous route Lincoln was able to claim citizenship of the Empire.