The phrase "with a lid on" is commonly used to refer to a container or object that has a cover or cap on top to protect the contents inside. However, alternative phrases can also be used to convey the same meaning, such as "covered," "sealed," "capped," "topped," "enclosed," or "shut." Each of these synonyms can be used interchangeably with the phrase "with a lid on" depending on the context and situation. Whether you're referring to a jar, a pot, or a box, these synonyms for "with a lid on" can make your writing or conversation more varied and interesting.