Mash 1/3 cup sugar and lemon peel in small bowl to blend well. DO AHEAD Lemon sugar can be made 3 days ahead. Cover and store at room temperature.
Bring 1/2 cup sugar, 1/2 cup water, honey, and lavender to boil in heavy small saucepan over medium-high heat, stirring until sugar dissolves. Reduce heat to medium and simmer until lavender flavor is pronounced, about 3 minutes.
Strain syrup into small bowl. DO AHEAD Can be made 1 day ahead. Cover and let stand at room temperature. Rewarm syrup before continuing.
Place berries in large bowl. Pour warm syrup over berries; stir to coat.
Divide berries and syrup among 8 bowls. Spoon crème fraîche over berries, sprinkle with lemon sugar, and serve immediately