Prepare the Raspberry Puree:

In a blender or food processor, combine the fresh raspberries, granulated sugar, and lemon juice. Blend until smooth.
Strain the mixture through a fine-mesh sieve to remove the seeds. Set aside.
Make the Mascarpone Cream:

In a mixing bowl, beat the heavy cream until soft peaks form.
In another bowl, whisk together the softened mascarpone cheese, powdered sugar, and vanilla extract until smooth.
Gently fold the whipped cream into the mascarpone mixture until well combined. Set aside.
Assemble the Tiramisu:

Dip each ladyfinger cookie into the brewed coffee briefly, then arrange a layer of dipped cookies in the bottom of a serving dish or individual serving glasses.
Spread half of the mascarpone cream mixture over the layer of ladyfingers.
Drizzle half of the raspberry puree over the mascarpone layer.
Repeat the layers with the remaining ladyfingers, mascarpone cream, and raspberry puree.
Cover and refrigerate the tiramisu for at least 4 hours, or overnight, to allow the flavors to meld.
Serve and Garnish:

Before serving, garnish the tiramisu with fresh raspberries and a dusting of cocoa powder.