The phrase "with lid on" can be used to describe a variety of objects. Some useful synonyms to replace this phrase include "covered," "sealed," "closed," and "topped." These words are especially useful when describing containers or vessels that need to be closed tightly to prevent spillage or preserve freshness. Other synonyms that may be used in different contexts include "capped," "shut," and "enclosed." By using a variety of synonyms, writers can add variety and interest to their descriptions while still conveying the same idea. It is important to choose the most appropriate word based on the context in order to accurately convey the intended meaning.