In a blender, whirl strawberries and simple syrup to a purée. Strain into a serving pitcher.
To the pitcher, add lemon juice, gin, and half the Champagne. Stir in the sliced strawberries (to help settle the foam before pouring the rest). Twist lemon peels over the cocktail to release their oils, then drop into the pitcher. Pour in remaining Champagne and stir. Add more ice to chill, and serve immediately.