Rinse grape leaves under cool water, pat dry, and snip off any thick stems.

In a skillet, warm the olive oil over medium heat. Add the onion and cook until soft, about 5 minutes. Remove from heat and stir in the rice, dill, mint, lemon juice, salt, and 1/2 cup of the water. Let the mixture rest for 10 minutes.

Place a grape leaf on your work surface, vein side up. Place about 1 tablespoon of filling near the stem end, fold the bottom over the filling, fold in the sides, and roll tightly toward the tip. Repeat with remaining leaves and filling.

Line the bottom of a large pot with a few extra grape leaves. Pack the rolled dolmas, seam side down, in snug layers. Pour the remaining 1 cup water and a drizzle of olive oil over the top. Place a heatproof plate on top to keep them submerged. Bring to a gentle simmer over low heat, cover, and cook for 45 to 50 minutes, until the rice is tender.

Remove the plate, transfer the dolmas to a serving platter, and drizzle with a little more olive oil and lemon juice. Serve warm or at room temperature.