In a blender, combine the sliced strawberries and sugar. Blend until smooth.
Strain the strawberry mixture through a fine mesh sieve into a large pitcher to remove the seeds, pressing with a spatula to extract as much juice as possible.
Add the freshly squeezed lemon juice to the pitcher with the strawberry juice. Stir well to combine.
Chop the basil leaves roughly and add them to the mixture in the pitcher. Stir gently to release the basil's aromatic oils.
Pour in the cold water and mix until everything is well combined. Taste and adjust sweetness by adding more sugar if desired.
Refrigerate the lemonade for at least 30 minutes to let the flavors meld.
Serve over ice cubes and garnish with lemon slices and sprigs of basil.