Add the sugar to a large gallon-sized bowl. Rub sugar into the rinds of the lemons to access the flavorful oils in the skins. Then, juice the lemons into another bowl and set aside.
Pour hot water into the sugar. Stir until dissolved. The mixture should be thick and clear when the sugar is dissolved.
Stir in lemon juice, lavender extract and cold water. Refrigerate until cool, about 30 minutes or more. To serve, fill glasses with ice, then add vodka and top with lemonade.