1. Dislodge the grape leaves from the jar and separate them gently. Place in a large bowl in the sink and rinse under cold running water. Set aside in a colander to drain. Set aside.
2. Prepare the filling. Mix the rice, pine nuts, onions, lemon juice, and pepper together in a medium-size bowl. Add the dried mint by crushing it between the palms of your hands.
3. Prepare the sauce. Combine 1 tablespoon of the olive oil, 1½ cups cold water, and lemon juice in a large bowl. Add the dried mint by crushing it between the palms of your hands. Set aside.
4. Prepare the stuffed leaves. On a clean work surface, spread the grape leaves out 3 at a time with the underside (veins) facing up and the base pointing toward you. Place about 2 teaspoons of the filling on the bottommost center of each leaf, varying the amount according to the size of the leaf. Tightly roll the leaf up once, then fold each side in. Continue to roll upward, making sure that the sides are always folded and tucked inward. Repeat with the remaining leaves and filling.
5. Cover the bottom of a large skillet with a layer of the stuffed leaves packed tightly together (seam side down). Crisscross with another layer. Pour the sauce over the leaves. (There should be enough liquid to fully cover the stuffed leaves. If there is not, add just enough to cover.) Place a small plate directly on top of the leaves to keep them from unraveling while cooking. Cover the skillet with a tight-fitting lid.
6. Simmer for at least 2 hours over low heat; the leaves should be tender, not mushy or too stringy. Check the leaves every 30 minutes and, if all of the liquid is absorbed, add cold water and the remaining 2 tablespoons olive oil.
7. Serve at room temperature on a platter, alongside other appetizers and pita bread.