Meh, while following an Oath Code is a moderately lawful single trait, I don't think it's necessary that all Paladins are Lawful as a whole.
E.g., Oath of Ancients is all about [paraphrased] "loving life, *not* belief in principles of honor, courage, and justice." An Ancients Paladin could very easily be any type of Good - Lawful, Neutral, or even Chaotic. Whereas Oath of the Crown is definitely Lawful - "dedicate to serving society and the just laws that hold society together."
Using a non-real Oath example, anyone who makes an oath to destroy civilizations (e.g., eco-terrorist druids) would certainly be Chaotic, not Lawful just because of their oath.
