President Lincoln did not have a Secret Service detail. He did have a body guard, John Frederick Parker, who left his post outside of the door to the Presidential box in Ford's Theater which allowed John Wilkes Booth access to the Presidential box.
After President Lincoln's death, Mr. Parker was assign to be Mrs. Lincoln's body guard while she was moving from the White House. Mrs. Lincoln felt that it was Parker's fault that her husband was killed and dismissed him from her presence.
The Secret Service was not implemented until July 5, 1865, and not for the reason which you would think.
The secret service's first job was for the Dept. of the Treasury to help suppress counterfeit currency.
After the assassination of President William McKinley in 1901, the Secret Service assumed the responsibility of full-time protection of the president in 1902.