You got it backwards, the CIA cannot lawfully operate within the United States, they however can operate lawfully within any foreign territory.
Their mandate is based on US law not whichever country they operate in, if they are caught they will be charged with espionage.
There is no such thing as a legal CIA operation, it might get permission from the host nation to operate but it doesn't make it a legal act in the nation in question.
If MI6/5 whoever gives the CIA permission to rendition or even assassinate a target from the UK that doesn't mean it's legal according to UK law.
Intelligence agencies operate in grey areas where there is an agreement in place as long as no one gets caught and most things are either kept so secret that no one would ever get to them or there is simply no paper trail at all.
The UK knows very well who is that CIA station chief in London despite them being there under false pretences which is a violation of UK laws, same goes for most of the CIA / any other TLA agency staff operating in a diplomatic mission under cover.
They all get some US State Department BS title and assignment and diplomatic papers but in reality they aren't diplomats and any competent nation knows all if not the majority of the TLA staff stationed in the US missions operating within it's borders.
Their mandate is based on US law not whichever country they operate in, if they are caught they will be charged with espionage.
There is no such thing as a legal CIA operation, it might get permission from the host nation to operate but it doesn't make it a legal act in the nation in question.
If MI6/5 whoever gives the CIA permission to rendition or even assassinate a target from the UK that doesn't mean it's legal according to UK law.
Intelligence agencies operate in grey areas where there is an agreement in place as long as no one gets caught and most things are either kept so secret that no one would ever get to them or there is simply no paper trail at all.
The UK knows very well who is that CIA station chief in London despite them being there under false pretences which is a violation of UK laws, same goes for most of the CIA / any other TLA agency staff operating in a diplomatic mission under cover.
They all get some US State Department BS title and assignment and diplomatic papers but in reality they aren't diplomats and any competent nation knows all if not the majority of the TLA staff stationed in the US missions operating within it's borders.