Lawful is not a requirement, nor is Good, for Any paladin.
An Oath is required, and your oath becomes a Law when breaking it incurs consequences.
Pretty sure that at the very least implies "lawful".
This seems pretty logical to me. I always thought lawful not as following and obeying the law of men, but as an opposition to chaos. Paladins perfectly organize their life against their oath which propells them to avoid chaotic influences and even abandon some portion of their feelings while making an act. That immediately pushes all of them, except for an oathbreaker, into the lawful category.
