put the lid on vs shut down

put the lid on

shut down

verb
  • To pass (another vehicle), especially quickly. 

  • To close, terminate, or end. 

  • To turn off or stop. 

  • To emotionally withdraw into oneself as a defense mechanism; to block out external stressors. 

How often have the words put the lid on and shut down occurred in a corpus of books? (source: Google Ngram Viewer )