Combine 8 oz blackberries, sugar, and lemon juice in a medium saucepan over medium heat. Cook, stirring occasionally, until berries break down and mixture thickens slightly, 8-10 minutes. Press through a fine-mesh sieve to remove seeds, then cool completely. Reserve remaining 4 oz blackberries for layering.

In a large bowl, beat egg yolks and sugar with an electric mixer on medium-high speed until pale, thick, and doubled in volume, about 3-4 minutes. Add mascarpone and beat on low until just combined and smooth.

In a separate bowl, whip heavy cream to stiff peaks. Gently fold whipped cream into mascarpone mixture in two additions until no streaks remain. Do not overmix.

Quickly dip half the ladyfingers into cooled espresso and arrange in a single layer in a 9x9 inch dish. Spread half the mascarpone cream over top, then drizzle with half the blackberry compote. Scatter half the reserved fresh blackberries over the cream.

Repeat with remaining ladyfingers, espresso, mascarpone cream, and blackberry compote. Cover tightly and refrigerate at least 4 hours or overnight. Dust with cocoa powder just before serving, and garnish with remaining fresh blackberries.