Warm 3 tablespoons of the olive oil in a large sauté pan over medium heat. Add the onions and sauté until translucent, about 5 minutes. Add the garlic and rice and sauté, stirring often, until the grains are well coated with the oil, about 5 minutes. Add the spinach, dill, tomatoes (if using), salt, pepper, and water and raise the heat to high. Bring to a boil, stirring and pushing the spinach down into the pan as it wilts. Reduce the heat to low, cover, and cook until the liquid is absorbed and the rice is tender, 15 to 18 minutes. Remove from the heat and let rest, covered, for 5 to 10 minutes.
Spoon the rice into a serving dish. In a cup, stir together the remaining 3 tablespoons olive oil and the lemon juice and drizzle the mixture over the rice. Serve hot or at room temperature.