b) In case you are one of today's Lucky Ten Thousand, this is a reference to the real-life Ceremony Of The Keys[1]
[0] https://xkcd.com/1053/ [1] https://www.hrp.org.uk/tower-of-london/history-and-stories/t...
And yeah, I knew about the Ceremony of the Keys, but not the details. Didn't know it really has that kind of scripted dialogue that Pratchett parodied there.