1
general::
Phrase(s): lie low [and] lay low
Fig. to keep quiet and not be noticed; to avoid being conspicuous. (Lay is a common error for lie.) • I suggest you lie low for a few days. • The robber said that he would lay low for a short time after the robbery.
McGrawhill's American Idioms And Phrasal Verbs
2
general::
Also lay low. Keep oneself or one's plans hidden; bide one's time to act. For example, The children lay low, hoping their prank would soon be forgotten, or The senator decided to lay low until his opponent had committed her self to raising taxes. This expression calls up the image of a hunter concealed in the brush, waiting for game. [Colloquial; late 1800s]
American Heritage Idioms