Your prayer reflects a heart that longs for what God Himself longs for, truth and righteousness, and it is right to bring that burden before the Father in the name of Jesus.
That thirst you describe is at its deepest a thirst for God. Every person carries it, whether they recognize it or not. We have physical needs and emotional needs for love and purpose and security, but beneath them all is a spiritual thirst that only God planted and only God can satisfy. People try to fill it in many other ways, with achievement, position, knowledge, even with keeping the law, but Jesus said that if you drink of that water you will thirst again. It does not satisfy. He stood and cried, if anyone thirsts, let him come to me and drink. He was speaking of that deep thirst of the soul, and He alone can quench it because He is God. When we pray for those who are caught in lies or who disregard human life and honest communication, we are praying that they would recognize that their true need is for Him.
You are also right to see that education and knowledge of the law cannot make a person righteous. Scripture says all have fallen short of the glory of God. A zeal for good or a mastery of legal study does not produce righteousness before God. The righteousness that God accepts is not our own righteousness established by our works, but the righteousness of Christ given to us when we put our faith in Him. God counts faith for righteousness. Christ is the end of the law for righteousness to everyone who believes. That is why your prayer from Psalm 51 is so fitting. God does not delight in outward sacrifice alone, but in a broken spirit and a contrite heart, which He will not despise. Only when a heart is broken over sin and turns to Jesus can it be taught to love truth and to act with true compassion and justice.
It is humble and good that you do not pray with boasting or with contempt, but with grief and mercy. Jesus said blessed are those who hunger and thirst for righteousness, for they shall be filled. That promise holds for you as you intercede, and it is the promise we ask God to fulfill in those you mentioned. We can ask Him to stir their hearts, to show them their sin so that they hate it and turn from it, and to draw them to the truth that sets free, which is found in Christ alone. The Father is seeking those who will worship Him in spirit and in truth, and the Holy Spirit is interceding even when we do not know how to pray as we should.
Continue to pray relentlessly as you have. God preserves those who are His, He sows light for the righteous and gladness for the upright in heart, and He will establish His kingdom in righteousness and judgment. Even when we see injustice now, we can trust that He is good, His mercy endures, and His truth stands through all generations. May He cover those who belong to Christ with peace and understanding, may He grant repentance and new hearts to those who are still bound in darkness, and may He fill you with hope as you wait for His will to be done.