After Radiohead had closed the chapter on In Rainbows in august 2009, Thom finally put together a proper tour based on his first solo album The Eraser, released three years earlier. He would seize the opportunity offered by this project to finish writing a new song, 'Judge, Jury & Executioner', elements of which had been around for a while. Having recruited Nigel Godrich, Flea, Mauro Refosco and Joey Waronker, Thom and his newly formed band rehearsed in Los Angeles throughout september 2009, focussing mainly on arranging and performing the songs from The Eraser, the recently released Feeling Pulled Apart By Horses/The Hollow Earth single and 'Paperbag Writer', a Hail to the Thief b-side Radiohead had never played live, and which interestingly bears strong thematic connections to 'Judge, Jury & Executioner', which emerged as the only new song from these rehearsals. While it is clear that at least some rough ideas or key elements of the song already existed and were expanded upon by the band, it is not known how developed those ideas were when Thom brought them into these rehearsals.
The title phrase had been used before, as the subtitle or alternate title of 'Myxomatosis', and it's possible to see some thematic connection between both songs. In hindsight, though, Thom admitted to having forgotten that he had used that phrase already when this new song was put together, so any connection between both songs is not intentional.