In a large pitcher, pour in the cold water and freshly squeezed lemon juice. Stir well to mix.
Stir in the lavender simple syrup until fully combined. I recommend starting with 1 ½ cups of simple syrup and adding more to fit your sweetness preferences.
Sprinkle in the sea salt and cream of tartar. Stir until everything is dissolved.
Refrigerate for at least 30 minutes, then serve over ice with lemon slices or lavender sprigs for garnish.