I'm going to say this once: NO LG character should be fine with slavery. Period. Remember, you're both Lawful AND Good. Slavery is NOT a good institution: it's rife with abuse even under the best of circumstances. A LG paladin should be planning to spur any society who accepts slavery into getting rid of it by lawful means -- challenging slaveholders to duels, for example, in a society that accepts dueling. It can be hard, but a paladin should take any and all chances to aid slaves that don't involve chaotic actions. If you run into escaped slaves? help 'em; you're freeing them from durance vile. If you are an escaped slave? Well we already covered that -- slavery is an evil institution, and therefore deserves no respect.
