In a medium saucepan over medium heat, combine 1 cup of raspberries and ½ cup of water. Simmer for about 5 minutes, crushing the berries. Strain through a fine mesh sieve, discard solids, and return juice to saucepan. Add ¾ cup sugar and 2 tablespoons lemon juice. Simmer 5 minutes until thickened, then chill.

In a large mixing bowl, whip 1 cup of heavy cream on medium-high until stiff peaks form (3-5 minutes). Set aside.

In the same bowl, combine 8 ounces mascarpone cheese, ¼ cup sugar, ⅓ cup chilled raspberry syrup, and 1 teaspoon vanilla extract. Beat on low until smooth (1-2 minutes). Fold in whipped cream until no white streaks remain.

Dip ladyfingers into chilled raspberry syrup for 2-3 seconds. Layer dipped ladyfingers in a dish, spread half of the mascarpone filling, and sprinkle half of the grated white chocolate.

Repeat the process for a second layer. Finish with remaining mascarpone filling and top with remaining white chocolate. Cover and refrigerate for at least 6 hours or overnight.