Add the raspberries and water to a medium saucepan over medium-high heat. Crush the berries with a potato masher or fork.

Bring the berries to a simmer, then reduce the heat to medium-low. Simmer for about 2 minutes.

Remove the saucepan from the heat. Pour the berries through a fine-mesh strainer positioned over a glass measuring cup.

Press the berries with the back of a ladle or spoon to extract as much juice as possible. Discard the seeds.

Return the raspberry juice to the saucepan. Add the sugar and lemon juice.

Bring the mixture to a boil, then simmer for 4–5 minutes, until it reduces slightly.

Remove from the heat and refrigerate until completely cool.

Add the heavy cream to a stand mixer fitted with the whisk attachment. Whip until stiff peaks form.

Transfer the whipped cream to a separate bowl.

Fit the mixer with the paddle attachment. Add the mascarpone, sugar, cooled raspberry syrup, and vanilla.

Beat on high until the mixture is smooth and well combined.

Add about 1 cup of the whipped cream and beat until incorporated.

Gently fold in the remaining whipped cream until the filling is light and fluffy.

Working one at a time, dip the ladyfingers into the cooled raspberry syrup. Soak them enough to soften without making them soggy.

Arrange the soaked ladyfingers in an even layer in an 8-inch square baking dish.

Spread half of the mascarpone filling evenly over the ladyfingers.

Finely grate half of the white chocolate over the filling using a zester, microplane, or fine cheese grater.

Add another layer of raspberry syrup-soaked ladyfingers.

Spread half of the remaining filling over the ladyfingers.

Transfer the remaining filling to a pastry bag fitted with a large round tip, or use a zip-top bag with one corner snipped off.

Pipe the filling evenly over the top of the tiramisu.

Grate the remaining white chocolate over the surface.

Cover and refrigerate for at least 6 hours, preferably overnight, so the layers can fully set and the flavors can meld.