In a medium saucepan, combine the chopped strawberries, granulated sugar and 1 cup of water. Bring to a boil over medium heat, stirring occasionally. Once it reaches a boil, reduce the heat and let it simmer for about 10 minutes, until the strawberries are soft and the sugar is dissolved.
Remove the saucepan from the heat and let it cool slightly. Transfer the strawberry mixture to a blender and blend until smooth. Strain the mixture through a fine-mesh sieve into a bowl, pressing down to extract as much liquid as possible. Discard the solids.
Using a citrus squeezer, juice the lemons. In a large pitcher, combine the fresh lemon juice and the strawberry syrup. Stir well to mix.
Add the 3 cups of cold water to the pitcher and stir to combine. Taste and adjust the sweetness or tartness by adding more sugar or water if needed. Refrigerate the lemonade until chilled, about 1-2 hours.
Just before serving, add the sparkling water to the pitcher and stir gently. Fill glasses with ice cubes and pour the fizzy strawberry lemonade over the ice. Garnish each glass with lemon slices, fresh strawberries.