He is K's supervisor, and is the one who gave him a "Unit" in order to provide him the power he wants. It is unknown whether the two held anything other than a professional relationship, but K seemed to have been determined to fulfill Edward's orders at all costs, meaning that he might have been grateful towards him, at the very least.
The student of the Kouryou Academy and also his greatest rival. Because of Tooru's resolve in protecting his friends resemble his (presumably) past self, K is extremely disgust over Tooru as he mocks Tooru's value of friendship and even willing to hurt his friends in order to break Tooru, both physically and mentally.
During the mission to retrieve Lilith for <<Equpiment Smith>>, K spoke to Lilith with respect and courtesy. However he was not above resorting to cruel methods if needed in order to fulfill his mission.
When the two of them met again, he asked Lilith to let him take Sakuya, since she was not the goal of his mission this time. However Lilith refused to comply to his demands, forcing him to attack her and knock her unconscious before taking Sakuya.