A lid is the top of a box or other container which can be removed or raised when you want to open the container.

Your lids are the pieces of skin which cover your eyes when you close them.

If you say that someone is keeping the lid on an activity or a piece of information, you mean that they are restricting the activity or are keeping the information secret.

If you say that you want to keep a lid on the cost of doing something, you mean that you want to prevent it costing you more than you feel is reasonable.