What is the origin of the idiom "lie like a rug" and when to use it?

The idiom "lie like a rug" originates from the association of rugs or carpets with a smooth and flat surface. The phrase suggests that someone is lying in a manner that is exceptionally deceptive or untruthful, much like a perfectly laid rug that conceals the imperfections beneath. This expression is used to imply that the person is skilled in distorting or fabricating the truth, often with the intention to manipulate or deceive others.