The correct response is: The object's potential energy will increase.
When Lucy lifts the object above her head, she is increasing its height relative to the ground, which increases its gravitational potential energy. The potential energy of an object is given by the formula \( PE = mgh \), where \( m \) is the mass, \( g \) is the acceleration due to gravity, and \( h \) is the height above a reference point. As the height \( h \) increases, the potential energy also increases.