The U.S. killing of Osama bin Laden in Pakistan was lawful under both U.S. domestic law and international law. The U.S. government's legal rationale will be similar to arguments used by both the Bush and Obama administrations to justify drone strikes against other al-Qaeda leaders in Pakistan and elsewhere. The Authorization to Use Military Force Act of September 18, 2001, authorizes the president to use "all necessary and appropriate force" against persons who authorized, planned, or committed the 9/11 attacks.
The killing is not prohibited by the longstanding assassination prohibition in Executive Order 12333 because the action was a military action in the ongoing U.S. armed conflict with al-Qaeda and it is not prohibited to kill specific leaders of an opposing force. The assassination prohibition also does not apply to killings in self-defense. The executive branch will also argue that the action was permissible under international law both as a permissible use of force in the U.S. armed conflict with al-Qaeda and as a legitimate action in self-defense, given that bin Laden was clearly planning additional attacks.
Some critics of the administration's legal theory that the United States is in an armed conflict with al-Qaeda might--if they were consistent with their past criticisms--argue that the United States did not have a right to use military force against bin Laden outside of Afghanistan, and that Washington should instead have sent an extradition request to Pakistan or asked the Pakistani government to arrest bin Laden. But such traditional critics may prefer to remain silent in this instance.
In addition, under the UN Charter, the United States would normally be prohibited from using force inside Pakistan without obtaining Pakistan's consent. It is not clear whether the Obama administration received the consent of the Pakistani government to use force inside Pakistan in this case, but the Pakistani government appears at least to have consented after the fact to this potential infringement of its sovereignty.