Heat 1/3 cup olive oil in a large skillet or dutch oven. Sauté onion until softened. Add lamb and cook until browned. Add pine nuts, rice, lemon juice, and 1/3 cup olive oil, stirring to coat and combine. Mix in mint, dill, and parsley.
To prepare the grape leaves, rinse in cool water. Drain and separate, laying each leaf stem-side up on paper towels to dry. Set aside damaged leaves to use when steaming.
While the leaves dry, remove long stems. Place a teaspoon of filling on the underside of each leaf. Roll gently, bringing both sides to the middle and then rolling up the center.
Place damaged leaves into the bottom of a pot, covering with 1 tbsp of olive oil. Lay rolled dolmas shoulder to shoulder, making a second and third layer as necessary. In the meantime, bring broth to a boil in a small sauce pot. Cover dolmas with broth and remaining olive oil. Weigh the top of the dolmathes down with plate so they won’t float up. Simmer for 45 minutes, then remove from the pot and serve warm.