What the Law does is show us how far short we fall. Law uses judgement to establish justice by handing out just punishments and just rewards, and by vindicating those who are in the right. This is true of both human and divine government. The bible teaches in many places that God will punish wrongdoing, and judge between his people and those who oppress them. But Law cannot motivate love, nor can it result in salvation, for no one perfectly keeps the law of God.
Law convicts but only grace can save and produce works of righteousness and justice.
Finally, I want to end by saying that our justification, though it is by God's mercy and grace alone, results in a just lifestyle. Though we are not justified by lawkeeping, justification results in lawkeeping and not in lawlessness. Rather, we uphold the law. Don't think that because you are a Christian you are free to do whatever you please. You are not.