To better illustrate my point picture an angel of Tymora whose ordered to roll a D20 seven times and for each 20 to give a mortal 200 gold, for each 19-2 a sack of candy, and for each 1 an apple. This is a Chaotic Good order from a Chaotic Goddess of Luck to a Lawful Good Angel she created.
This Angel, let's call her Casino, has two opinions, to obey and to disobey, but her choice is distracted by her Lawful Good nature to take the most Lawful Good choice.
If Casino refuses she has ignored her place in the divine hierarchy, defied her rightful authority figure, refused to do an act of good, and violated spiritual law by refusing her Goddess. This is Chaotic Neutral act at best, perhaps even Chaotic Evil even, even if it's driven by distaste for a Chaotic act of charity by random chance.
But if Casino obeys she is obeying divine law, respecting her place in the divine hierarchy, respecting her "Mother" and serving the words of her God and helping those in need, acting with generosity. It's both a Lawful and Chaotic act at the same time, but it's lawfulness far outweighs is chaoticness.
Another example The Angel Kitten, servant of Sharess is ordered to seduce lonely mortals, but the Kingdom has a law against sex with beings from outside the material plane and so to do so she has to violate human laws. (this also assumes Kitten consents and wants to do this because there is nothing inheritance unlawful about sex, and she still shares in the none unlawful elements of Sharess' own nature)
Sharess is the Goddess who created Kitten, her word is divine law, which in the hierarchy of laws is higher then mortal laws, so obeying Sharess is a Lawful act despite violating human laws, because it respects both a higher moral form of law, divine law, and respects the hierarchy of laws, respects the authority of Sharess, and it avoids disobeying her mistress so a Chaotic act is avoided. There for breaking the human law is the Lawful Good act, but it appears to be a Chaotic act to an outsider.
The most Lawful Good act is to always obey the more moral and hierarchical authority over a lesser authority, especially if its the authority of one's God the highest authority to an Angel vs the Authority of anything else. Only true universal Chaotic evil acts would trump this as then disobedience becomes the less Chaotic less evil act.