Make the simple syrup: Combine the sugar and 1 cup water in a small saucepan. Bring just to a simmer over medium heat, stirring until the sugar dissolves, 2–3 minutes. Remove from heat and cool to room temperature, about 15 minutes.
Prepare the strawberries: Rinse and hull the strawberries. Add them to a blender and blend until very smooth, 30–60 seconds.
Strain the puree: Pour the strawberry puree through a fine-mesh sieve into a large pitcher, pressing to extract as much liquid as possible; discard the seeds and pulp.
Mix the lemonade: Stir in the cooled simple syrup, the freshly squeezed lemon juice, and 4 cups cold water until evenly combined.
Chill: Refrigerate until cold, at least 30 minutes, or until well-chilled to your liking.
Serve: Fill glasses with ice, pour in the strawberry lemonade, and garnish with lemon slices. Serve immediately.