What does Luke 18:2 mean?
This begins the parable of the persistent widow. Jesus has promised to return and judge the sins of humanity. The disciples seem discouraged that this will take longer than they had hoped (Luke 17:22—18:1). Jesus wants them to keep praying: looking to God who is sure to act on behalf of His elect (Luke 18:1–7).The parable begins by describing the antagonist. In that cultural context, a judge who doesn't fear God is an almost ridiculous paradox. God gave Moses the law by which judges of Israel were to make rulings. He requires that all people act justly (Deuteronomy 16:19; Micah 6:8). Those who do not fear Him are the definition of fool (Proverbs 1:7). Under that view, what Jesus describes is meant to be deliberately extreme. A parallel to modern courts might be to speak of "a reckless, lawless judge."
In addition, this judge does not respect people. This means he shows no deference nor regard. He is not described as someone who takes bribes. Yet he's identified as lacking compassion, with just enough power to not feel threatened by criticism. His power would allow him to make fair judgments, but he simply doesn't care.
A widow comes before him, demanding her adversary face legal repercussions. The Mosaic law says, "You shall not pervert the justice due to your poor in his lawsuit" (Exodus 23:6). If a judge despises God and people, he can't be expected to care about a widow, but he does care about his own comfort. When the widow refuses to back down, he finally acts (Luke 18:3–5).