In a medium saucepan, combine 1 cup of raspberries with 1/2 cup of water over medium heat. Simmer for about 5 minutes, gently crushing the raspberries. Strain to remove seeds, then return juice to pan. Stir in 1/2 cup of granulated sugar and 1 tablespoon of lemon juice; simmer for an additional 5 minutes. Cool completely.

In a large mixing bowl, beat 1 cup of heavy cream with an electric mixer on high speed until stiff peaks form, about 3-4 minutes. Set aside and keep chilled.

In another bowl, combine 1 cup of mascarpone cheese, 1/4 cup of granulated sugar, 1/4 cup of cooled raspberry syrup, and 1 teaspoon of vanilla extract. Beat until smooth and creamy, about 2 minutes. Gently fold in the whipped cream until homogenous.

Dip 12 savoiardi ladyfingers quickly in the cooled raspberry syrup. Arrange half of the soaked ladyfingers in a single layer in an 8-inch square dish. Spread half of the mascarpone filling over the ladyfingers, then sprinkle half of the grated white chocolate on top. Repeat the layers with remaining ingredients.

Cover the assembled tiramisu tightly with plastic wrap and refrigerate for at least 6 hours, ideally overnight.