Preheat oven to 375°F. In a large skillet, heat oil on medium-high. Add garlic and spinach and cook for 1 –2 minutes, until spinach is just wilted. Transfer to a colander, allow to cool for 2–3 minutes and gently press to drain excess water. Cool to room temperature and transfer to a large mixing bowl. Set aside.
Add mozzarella, yogurt, cream cheese, lemon juice and cayenne to the bowl and combine with spinach garlic mix. Stir in lobster, brie, chives and parsley. Season with salt and pepper.
Transfer dip to a shallow ovenproof cast iron skillet with cover or dutch oven place dish on a hot grill, covered. Heat for 15–18 minutes, until hot and bubbling. Remove from grill and let rest for 3–4 minutes.