Put the onions and oil in a skillet and cook over medium heat until the onions are soft and translucent, about 10 minutes. While the onions cook, peel the garlic cloves and mash them to a paste in a mortar and pestle. Add this to the pan along with the tomato, lemon juice, tomato paste, and salt and pepper to taste. Cook for another 5 minutes. Stir in the rice. Remove the pan from the heat and stir in the dill. Set aside to cool to room temperature, then refrigerate.
While this is cooling, drain the grape leaves and carefully pull them apart. Put them into a bowl and cover them with cold water. Let them soak until you are ready to roll.
Heat the oven to 350 degrees F.
Place a grape leaf on your work surface, shiny side down. Add 1 tablespoon of the rice mixture to the middle of the grape leaf. Fold the sides over the rice and roll the leaf into a small log shape, about the size of George's thumb. Repeat with the remaining rice, placing the stuffed leaves into a 9 by 9-inch baking dish. When the dish is full, cover the stuffed leaves with several layers of flat grape leaves and pour in 1 cup of water. Cover and bake for 1 hour. Let cool to room temperature and refrigerate. Serve cool.