What did Lord Krishna mean by telling Arjuna that he needs to have peace by becoming one with himself and soul?
I think that the basic premise in the "divine song" is how to overcome division. It is division that causes Arjuna the greatest amount of hurt. He feels divided on the battlefield between what he must do and the people he see around him, people he knows and loves. He feels division between what his responsibility is and what he feels in his heart. Arjuna feels fundamental division in the mere exposition to the Bhagavad- Gita. He is in the middle of both warring factions, about to fight, prepared for battle. He feels division because he feels on the outside of this. It is for this reason that he puts down his arms, existentially agonizing about who he is and where he is in the world.
Lord Krishna is his charioteer. This takes on a spiritual dimension in the "divine song" in terms of how he works with Arjuna. Essentially, Lord Krishna's message to Arjuna is meant to overcome division. If Arjuna is able to detach himself from seeking or examining the fruits of his labor and submit his own will to Lord Krishna, division is overcome and unity is achieved. This becomes the basic message that Lord Krishna gives to Arjuna. The ability to acquire peace comes from this detachment to the fruits of one's labor. When one is fixated on the fruits of individual labor, then one is divided between the work they do and its outcome. Lord Krishna argues that when individuals are focused on the fruits of labor, then the condition of being forlorn is evident as we have sacrificed what is immortal and transcendent for that which is temporary. The "now" is seen as eternal and the eternal is misplaced. This is where Arjuna is and for Lord Krishna, the ability to understand this condition and rectify it by submission through the Lord is where peace can be evident. When Lord Krishna reminds Arjuna to place all worries at his feet and simply submit to the will of the divine as opposed to worrying about "the now," a path is offered through which Arjuna can find peace and become one with himself and the true nature of his soul: "Giving up all vexations and paths, do thou take refuge unto Me. I will save you from all dangers." It is here in which Lord Krishna wishes to change the focus of Arjuna, compelling him to understand the need to take action and relinquish the dwelling on consequences, the fruits of one's labor. Through this, a path for unity and peace is laid down for Arjuna and us.