In a blender, combine strawberries and basil leaves with 1/2 cup cold water. Blend until smooth.
Strain the strawberry basil mixture through a fine sieve to remove the solids.
In a large pitcher, combine the strawberry basil juice with lemon juice, sugar, and the remaining 2 1/2 cups of cold water. Stir well until the sugar dissolves.
Serve the lemonade over ice and garnish with extra basil leaves and strawberry slices if desired.