In a medium saucepan, combine raspberries and water over medium-high heat. Simmer until bubbly, then strain mixture to remove seeds, returning juice to the pan. Add sugar and lemon juice, boil briefly, then simmer until thickened for about 4-5 minutes. Set aside to cool completely.

In a stand mixer, whip heavy cream until stiff peaks form, about 3-5 minutes. In another bowl, beat mascarpone, sugar, raspberry syrup, and vanilla until smooth. Gently fold whipped cream into mascarpone mixture until combined.

Quickly dip each ladyfinger into raspberry syrup and layer them in an 8-inch dish. Drizzle with remaining raspberry syrup, then spread half the mascarpone filling on top. Sprinkle grated white chocolate over fill.

Repeat layering with remaining ingredients, dipping ladyfingers and assembling. Consider using a piping bag for the final layer of mascarpone filling.

Cover with plastic wrap and refrigerate for at least 6 hours, preferably overnight, to set and meld flavors.