Step 1: Prepare the Simple Syrup. In a small saucepan, combine 1 cup granulated sugar and 1 cup water. Heat over medium heat, stirring constantly, until the sugar is completely dissolved. Do not boil. Remove from heat and let cool completely to room temperature. You can also chill it in the refrigerator.
Step 2: Make the Strawberry Puree. Wash and hull the fresh strawberries, then slice them. Place the sliced strawberries in a high-powered blender or food processor. Blend until smooth. For a perfectly smooth, seed-free lemonade, pour the puree through a fine-mesh sieve into a bowl, pressing the solids to extract all the juice. Discard any remaining pulp. Chill the puree if not already cold.
Step 3: Assemble the Lemonade. In a large pitcher, combine the chilled strawberry puree and the freshly squeezed lemon juice. Stir gently to combine.
Step 4: Add Water and Adjust. Pour in 4 cups of cold filtered water. Stir well. Taste the lemonade and adjust the sweetness and tartness to your preference by adding more simple syrup (for sweetness) or additional lemon juice (for tartness) as needed.
Step 5: Serve. Fill glasses with ice cubes. Pour the strawberry lemonade into the glasses. Garnish with fresh lemon slices, whole strawberries, or a sprig of mint, if desired. Serve immediately and enjoy!