1 cup water, divided
1/3 cup white sugar
6 cups cubed seedless watermelon
1/2 cup red raspberries
1/2 cup fresh lemon juice
Combine 1/3 cup water and sugar in a small saucepan; bring to a boil, stirring constantly, until sugar dissolves. Remove simple syrup from heat to cool.
Place watermelon, raspberries, and remaining water together in a blender; pulse until smooth. Pour watermelon mixture into a frosted pitcher; stir in simple syrup and lime juice. Refrigerate until chilled, about 1 hour.