Lawful Good alignment does not reflect a characters overall attitude but rather how they go about doing their job based on their morality. Lawful Good means that a character chooses to help other good people but doing so without harming others that would deem 'unlawful' or without rectitude. Polite spy is a perfect example of this, since even though extremely hostile enemies may want to harm him, he does not retaliate. In contrast, as Chaotic Good person would have the same goal and intentions as a Lawful individual would, but they will be hostile to people who are evil or want to cause harm to themselves or their allies, and will not hesitate to kill such individuals.
I hope that clears things up.<ac_metadata title="Lawful Good alignment with regards to Polite Spy"> </ac_metadata>