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For the Simple Syrup, mix sugar and water in small saucepan. Bring to boil. Remove from heat. Add rosemary; let stand 10 minutes, stirring occasionally to dissolve sugar. Strain. Cover and refrigerate until well chilled.
Cut 4 of the lemons in half crosswise. Cut remaining 2 lemons into slices. Grill lemon halves and slices over medium heat 4 to 5 minutes or until lightly charred. Set lemon slices aside for garnish. Squeeze juice from lemon halves to yield 1/2 cup juice.
Place watermelon cubes and lemon juice in blender container; cover. Blend on high speed until smooth. Pour fruit mixture into large pitcher. Add Simple Syrup and cold water; mix well. Serve in ice-filled beverage glasses. Garnish with reserved lemon slices.