In a small saucepan, combine the strawberries, sugar, and 1 cup of water. Bring to a gentle simmer over medium heat, stirring occasionally.
Cook for 3 to 5 minutes, until the strawberries soften and release their juice. Remove from heat and let cool slightly.
Blend the strawberry mixture until smooth, then strain through a fine-mesh sieve if you prefer a smoother lemonade.
In a large pitcher, combine the strawberry puree, lemon juice, and remaining 3 cups of cold water. Stir well.
Add ice and chill for at least 10 minutes. Serve over more ice and garnish with mint if desired.