Once the four component item quests (Ponze of Flesh, A Treasured Mother, Method in His Malice, Labor of Love) are unlocked and completed they can be repeated immediately. You do not need to have another weapon at Nexus to access them.

LaylaTsarra was commenting on the fact that she was waiting to max her light on her 3rd relic before starting on the dungeon farming for her 3rd set of zodiac components.