a lid on sth
*a lid on something
1. Lit. a cover on something, such as a pot, pan, etc. (*Typically: get ~; keep ~; put ~.)
Keep the lid on the pot until the stew is almost done.
Put the lid on the skillet for just a little while.
2. Fig. a scheme to suppress a scandalous or embarrassing situation and keep it secret. (*Typically: get ~; keep ~; put ~.)
We can't keep the lid on this any longer. The press has got wind of it.