It is a temptation in English with its huge vocabulary to find false distinctions.
The "top" is a generic word that means "that which is most elevated relative to something considered in its socially conceived 'normal' orientation." To speak of the "lid" of the Empire State Building is to use language for humorous effect.
A "lid" is the top of a container, and usually a relatively relatively small container, although size is not a necessary criterion. For example, the hatches on an oil tanker are not usually referred to as "lids."
It is probably true that, in the context of modern packaging, lids usually have a screw-top or a pop-top, but that is (not yet at least) inherent in the word. A slang word for a hat or cap is a "lid", and few hats that I know of are screwed on to the heads of the wearers.
If you use "lid" to mean the part of a container meant to be opened in an orientation that does not result in the contents being precipitated toward the floor by gravity, you will seldom if ever go wrong.