With a vegetable peeler remove zest from 4 lemons and squeeze enough juice from these and remaining 2 lemons to measure 1 cup.
In a saucepan boil 1 cup water with sugar, stirring, until sugar is dissolved. Add zest, lemon juice, and remaining 1 cup water and cool.
In a food processor or blender puree blackberries and stir into lemonade. Pour blackberry lemonade through a sieve into a pitcher or other container and chill. Chill the lemonade, covered, at least until cold and up to 2 days.
Serve lemonade over ice in tall glass, garnished with lemon slices.
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