sit on the lid

[vil]

Dear teachers,

Would you be kind enough to give me your considered opinion concerning the interpretation of the expression in bold in the following sentence?

I’ve kept it out of the newspapers so far. I can’t sit on the lid much longer. We’re too well known socially and otherwise. (E. S. Gardner, “The Case of the Lazy Lover”)

sit on the lid = muffle, keep down, keep silent, suppress

V.

[Tdol]

I suppose it's an extension on keep a lid on something.