Place trimmed strawberries in a food processor or blender and puree. Strain the puree and discard the seeds.
Slice the lemons in half and squeeze each into a large measuring cup. Remove any seeds. You should yield approximately 1.5 cups of juice.
In a large pitcher, combine the lemon juice, sugar and strawberry puree. Stir in the cold water and serve over ice.
Notes
If you want to make a simple syrup to dissolve the sugar, add 1 cup of water to the 1 cup of sugar. Place in a small saucepan and simmer over low heat until the sugar is dissolved. Then add only 7 cups of cold water for your last step.