Cut 8 medium size lemon slices, cover and place in refrigerator. Peel and thinly slice 4 kiwis. Line a rimmed baking sheet with parchment paper. Arrange kiwi slices in single layer on prepared sheet. Place in freezer. Freeze until solid.
Peel, puree and strain 5 kiwis. Combine Gin, lemon juice, St. Germain, sugar, salt, kiwi puree and 3 cups ice in a large pitcher. Refrigerate until chilled. Stir club soda into pitcher. Pour cocktail into glasses, add a few frozen kiwis to each glass, garnish with lemon slices and serve.