In a saucepan, combine 1/2 cup of the water with 3/4 cup of the sugar and stir over moderate heat until dissolved, 2 minutes.
In a blender, working in batches, puree the watermelon with the sugar syrup and lemon juice until smooth. Pour the mixture into a 9-by-13-inch baking pan and freeze for 30 minutes. Using a fork, stir the granita; continue stirring every 30 minutes, until frozen and fluffy, about 3 hours.
Meanwhile, in a saucepan, combine the remaining 1/4 cup of water and 1/2 cup of sugar with the cardamom pods and bring to a boil. Simmer over moderate heat until the sugar is dissolved, 2 minutes. Remove from the heat and let stand for 5 minutes. Strain the syrup and refrigerate.
Fluff the granita with a fork. Scoop into bowls, drizzle with the cardamom syrup and serve immediately.
One Serving 202 cal, 0 gm fat, 0 gm sat fat, 55 gm carb, 1 gm fiber.