In a medium saucepan, combine fresh raspberries with water over medium heat, crushing the berries as they simmer for about 10 minutes. Strain the mixture through a fine mesh sieve, then stir in granulated sugar and lemon juice, bringing to a boil before removing from heat. Chill in the refrigerator for at least 30 minutes.

While the raspberry syrup cools, whip heavy cream in a large mixing bowl using an electric mixer until stiff peaks form, about 3-5 minutes. In a separate bowl, combine mascarpone cheese, sugar, vanilla extract, and ¼ cup of the chilled raspberry syrup. Beat until well combined and creamy. Gently fold in the whipped cream.

Take the chilled raspberry syrup and briefly dip each savoiardi ladyfinger into the syrup for no more than 2 seconds. Arrange in a single layer in an 8-inch dish. Spread half of the mascarpone filling over them and sprinkle with grated white chocolate.

Continue layering by dipping another batch of ladyfingers in the raspberry syrup, placing them atop the first layer. Spread the remaining mascarpone filling on top and sprinkle with more grated white chocolate. Cover with plastic wrap and refrigerate for at least 6 hours, or overnight.