Make the Raspberry Syrup:

Combine raspberries and water in a medium saucepan over medium-high heat. Crush the berries with a potato masher or fork. Bring to a simmer, then reduce heat to medium-low and simmer for about 2 minutes.

Remove from heat and strain the mixture through a fine-mesh strainer into a glass measuring cup, pressing to extract as much juice as possible. Discard the seeds.

Return the raspberry juice to the pan, add sugar and lemon juice, and bring to a boil. Simmer for about 4-5 minutes until slightly reduced. Chill in the refrigerator to cool completely.

Make the Filling:

Using a stand mixer with the whisk attachment, whip the heavy cream until stiff peaks form. Transfer whipped cream to a separate bowl.

In the mixer bowl with the paddle attachment, beat mascarpone cheese, sugar, ¾ cup raspberry syrup, and vanilla on high until combined. Add about a cup of whipped cream and continue beating until smooth. Gently fold in the remaining whipped cream.

Assemble Tiramisu:

Dip each ladyfinger in raspberry syrup until soaked but not soggy, and arrange them in an even layer at the bottom of an 8-inch square dish. Spread half of the mascarpone filling over the ladyfingers. Grate half of the white chocolate over the filling.

Add another layer of syrup-soaked ladyfingers on top of the filling. Spread the remaining mascarpone filling over the ladyfingers. Pipe the rest of the filling evenly over the tiramisu using a pastry bag with a large round tip or a ziplock bag with the corner cut off. Grate the remaining white chocolate on top.

Cover with plastic wrap and refrigerate for at least 6 hours, preferably overnight.