It’s true that the world offers a false sense of peace; and there have been many false prophets of peace in the past, saying “‘Peace, peace,’ . . . when there is no peace.” (Jer 8:11); even the Antichrist is likely to claim power through it (see Rev 13:3-4; 2 Thes. 2:4-9; Da 11:36). In the End, people will again falsely say “‘Peace and safety,’” before destruction suddenly comes upon them (1 Thes 5:3). But through Jesus, we can have true Peace with God, internal peace, peace with others, even our adversaries (including litigants), and peace between nations (with a real, and final fulfillment of it in His Kingdom). See Jn 14:27; 16:33; Rom 5:1; Eph 2:14; Rev 21-22.

In addition, how is Reconciliation tied to Justice?: If Justice is getting one’s due (i.e, for good or bad), reconciliation involves cancelling the debt (i.e., what is due); and so, without something due, the dictates of justice would seem to be fully satisfied (one could say justice is done, by removing the thing actually due). It isn’t a perfect system (only God’s Justice is), and inevitably involves compromise among sides who are each convinced they are right. And yet Jesus constantly reminds us to pursue this, to be quick to forgive and reconcile with our adversaries (Matt 5:25). It is simply superior, in many situations, to heed this, and avoid the devastating costs of litigation, or even war (even if one is in the right).