What is the meaning of Thy liberty in law?

It means that true liberty cannot and does not suggest the absence of law, but rather quite the opposite. It's through obedience to law that we are made more free, provided that the laws we obey are true laws and not just man's restrictions designed to control man. True laws conform to and reflect the truths of the universe in all its forms. Our role as humans is to discover these true laws and model our own laws and our forms of government after them.