Add strawberries, sugar, and lemon juice to a blender
Blend until smooth to make strawberry purée
Taste and adjust sweetness if needed
Fill a cocktail shaker with ice
Add Hennessy, strawberry purée, simple syrup, and lemon juice
Shake vigorously for 15–20 seconds
Fill a rocks glass or stemless wine glass with fresh ice
Strain cocktail into the glass
Garnish as desired and serve immediately