The phrase "lays low" refers to the act of hiding or staying out of sight to avoid attention or danger. Some synonyms for this term include "keeps a low profile," "remains inconspicuous," "lies low," "stays under the radar," "stays out of sight," "stays hidden," "remains unseen," "maintains a low profile," "stays incognito," "hides away," "keeps to oneself," "avoids detection," "stays off the map," "lies in wait," "remains elusive," "keeps off the radar," and "stays out of harm's way." These phrases are commonly used to describe behaviors or actions taken by individuals who wish to avoid unwanted attention or potential danger.