Popularized by CJ in The West Wing and used by the real US press secretary to signify that there is no more news to be given to the press. Saying "that's a full lid" is a neat way of telling someone you are done talking about something or have finished taking questions.
Thank you for your questions, that's a full lid
To manage the impossible; to boss it in the face of qualified doubt; to beat insane odds against you.
"England can 'do a Leicester' at this summer's Euros according to Foxes hero Danny Drinkwater" Article Headline in the Mirror (17/05/2016)