Were the target of a lethal operation a U.S. citizen who may have rights under the Due Process Clause and the Fourth Amendment, that individual's citizenship would not immunize him from a lethal operation.
Yet it was Congress that "authorized the President to use all necessary and appropriate force against ... al-Qa'ida and its associated forces," and it's only Congress, realistically, that can de-authorize him.
U.S. presidents do not relinquish acquired powers. It's neither in the nature of the beast nor his office. The Founders understood that, and, as mentioned, they anticipated and feared it, although their fears were tempered by the counterbalance of a responsible, conscientious Congress.
And there's the modern rub.