Traditional Paladins OD&D, AD&D were L/G, drawing power from a single deity, so going undercover is not in their repertoire. They would always speak the truth (as they see it), followed swiftly by martial enforcement, if appropriate.
I detest the idea of a Lawfull Stupid paladin - an image I see for too many people follow.
On the Lawfull vs Good axis, paladin should priority good over law. It makes no sense to fall for any chaotic action. For a CRPG developer, they should be as lax as possible with interpretations and limitations specifically because they cannot cover all the reasonings.
Paladins not capable of going undercover? I disagree. It is absolutely stupid to walk into a sleeping enemy den and wake them to challegne them to a fight or other IDIOTIC actions that some people think paladins MUST take.
