C). The object's potential energy will increase.
When Lucy lifts the object above her head, she is raising it against the force of gravity, which increases its height. The potential energy of an object is given by the formula \( PE = mgh \) (where \( m \) is mass, \( g \) is the acceleration due to gravity, and \( h \) is height). As the height \( h \) increases, the potential energy also increases.