In a medium saucepan, combine 2 cups of frozen raspberries, 3/4 cup of granulated sugar, and 2 tablespoons of fresh lemon juice. Heat over medium heat until bubbling and then reduce to a simmer, stirring occasionally for about 25 minutes until thickened.

In another saucepan, mix 1/2 cup of granulated sugar, 1/2 cup of water, and 1 cup of frozen raspberries. Boil while stirring until sugar dissolves, then let it simmer for 3 minutes. Strain through a fine-mesh sieve and cool completely.

In a large bowl, whisk together 1 cup of mascarpone cheese, 1/2 cup of powdered sugar, the juice of 1 lemon, and 1 teaspoon of vanilla paste until smooth. In a separate bowl, whip 1 cup of heavy cream to medium-stiff peaks and fold into mascarpone mixture.

Layer the dessert in a 9x9-inch dish starting with mascarpone cream, then soaked ladyfinger cookies dipped in raspberry syrup. Repeat layers until the dish is full, finishing with a layer of raspberry jam.

Cover with plastic wrap and refrigerate for at least 8 hours, preferably overnight. Serve garnished with fresh raspberries and lemon slices.