By skyforbes 
Grey Lanterns are formed after a person experiences catastrophic emotional grief and from harnessing the emotion of grief (Sadness, Pain, Yearning, etc.), turn it into a source of strength.
Those who have experienced true loss, have fallen into a deep depression that makes them feel nothing and have been made to feel completely hopelessness, are perfect candidates for being one.
The ring of a Grey Lantern is also formed from an object that makes them ruminate about their sadness and its origin.