Good should always supersede any other spectrum of alignment
Actually for a Lawful Good person... both Law and Good are equal (well OK, it depends on your character... but alignment wise both Law and Good are equally measured). No where in alignment did they even hint that Law-Chaos spectrum is secondary to Good-Evil.
A Lawful Good person who has to enact a harsh but strict sentence may have prefered a lighter sentence but understand the importance of upholding the law.
Law is about understanding that the law has purpose that order is important. A Lawful Good Paladin would be a character who could let a villain go free because that is the law.
For example lets say the villain went to trial and the Paladin KNOWS he is guilty and that he will just go back to doing evil things... but the trial found him innocent.
The difference between a Lawful Good character and a Chaotic Good character would be that the Lawful Good person may leave him alone (or reinvestigate... that would be the most likely action)... while a Chaotic Good person would likely ignore the trial and kill the villain. Afterall to a Chaotic Good character the law is only a barrier to the greater good. While to a Lawful Good character the law is the tool to the greater good.
Often the best way of thinking of it is that a Lawful Good character wants to use the law, honor, and commitment to do good.