Wiktionary
put a lid on it
vb. (context idiomatic English) (forceful) To be quiet; shut up; to stop talking about something or making noise.
Usage examples of "put a lid on it".
We'll cap it or put a lid on it and then I can take it with me when I go to the doctor and he can analyze it.
Every Pinko in the UAES knows what happened at Variety International the other day, and I say we put a lid on it and lull them to sleep.