Well, according to the Jewel Sword article, you will have better chances of getting drops by equipping the Ring of Arcana, although it will not affect the quality of the drops. Then again, the Lapis Lazuli grants a +20 LCK boost (+40 if you equip two).

Personally, I would favor equipping both Lapis Lazulis, although you may want to make some experimentation first and decide for yourself what's better, either by equipping one Lapis lazuli and one Ring of Arcana, or perhaps two Rings of Arcana (although I don't know if their effects actually stack).