Because the UK has a mutual legal assistance treaty with America, GCHQ can make an application through the US department of justice, which will make the approach on its behalf. - http://www.freerepublic.com/focus/f-chat/3538130/posts
Then conversely, DOJ can apply to GCHQ.
Executive order 12139. Surveillance WITHOUT a court order can be ordered by the Attorney General. (h/t Whenifhow) - https://www.archives.gov/federal-register/codification/executive-order/12139.html
Did Atny Gen Lynch request records from GCHQ?
As Peroit of Agatha Christi novels would say, "Exactement" Chief Inspector Jap. There is much mischief here."