Set a fine-mesh strainer over a bowl. In a blender, combine the strawberries and 1 cup of the water. Blend until smooth, then pass through the strainer to remove the seeds and foam.

Combine the sugar and another 1 cup water in a small saucepan over medium heat. Simmer, stirring, until the sugar dissolves. Set aside to cool to room temperature.

In a large pitcher, stir together the lemon juice, strawberry puree, sugar syrup, and the remaining 5 cups water. Chill in the refrigerator until ready to serve.

To serve, stir a few handfuls of ice into the pitcher. Pour into glasses with ice and garnish with strawberries and lemon slices.