In a small bowl, sprinkle the gelatin over the water and let stand until softened, about 5 minutes. In a small saucepan, combine the lime juice with 6 tablespoons of the sugar and simmer over moderate heat just until the sugar is dissolved, about 3 minutes. Remove from the heat and stir in the softened gelatin until melted. Transfer the lime gelatin to a medium bowl and let cool slightly. Whisk in the yogurt.