In a small saucepan, combine fresh or frozen raspberries and water over medium heat. Simmer for about 10 minutes, stirring occasionally, until the raspberries break down. Crush them with a fork and strain the mixture through a fine mesh sieve. Return strained juice to the saucepan, add granulated sugar and lemon juice, and simmer for an additional 5 minutes until slightly thickened. Chill completely in the refrigerator.

In a chilled mixing bowl, whip the heavy cream on medium-high speed until stiff peaks form, about 3 to 5 minutes. Gently transfer to another bowl and set aside.

In the same mixing bowl, beat the mascarpone cheese, granulated sugar, raspberry syrup, and vanilla extract on medium speed until smooth and creamy, about 2 minutes. Gently fold the whipped cream into the mascarpone mixture using a spatula.

Dip each savoiardi ladyfinger quickly into the chilled raspberry syrup. Arrange the soaked ladyfingers in a single layer at the bottom of an 8-inch dish. Spread half of the mascarpone filling evenly over the ladyfingers, then sprinkle half of the grated white chocolate on top.

Repeat the process by dipping another set of ladyfingers in the raspberry syrup and layering them over the first filling. Top with remaining mascarpone filling and grated white chocolate.

Cover the assembled tiramisu with plastic wrap and refrigerate for at least 6 hours, or overnight for the best results. Cut clean slices with a warm knife when ready to serve.