Combine 1/2 cup water and sugar over med- high heat and bring to boil. Cook for only 1 minute and then transfer syrup to a glass measuring cup and chill for at least an hour.
Combine remaining 1 cup water, sugar syrup, sorbet, orange juice, and lemon juice in blender and blend until smooth.
Pour 1 tsp of the grenadine in bottom of each glass. Pour in sorbet mixture, garnish with lemon slices and chill for at LEAST 30 mins. Serve straight up or on the rocks.