Combine 8 ounces of the mixed berries, sugar, lemon juice, and water in a small saucepan over medium heat. Cook for 5-7 minutes, mashing the berries with a spoon, until the mixture is jammy and the berries have broken down. Remove from heat and press through a fine-mesh sieve to remove seeds. Let cool completely, about 20 minutes.

In a large bowl, beat the cold heavy cream with an electric mixer on medium-high speed until stiff peaks form, about 3-4 minutes. The cream should hold its shape when you lift the beaters. Transfer to a separate bowl.

In the same large bowl (no need to clean it), beat the mascarpone, powdered sugar, and vanilla on medium speed until smooth and fluffy, about 1 minute. Do not overbeat or the mascarpone may curdle.

Gently fold half the whipped cream into the mascarpone mixture to lighten it, then fold in the remaining whipped cream until no streaks remain. The mixture should be thick and spreadable.

Spread a thin layer of mascarpone cream on the bottom of a 9x13 inch dish. Quickly dip each ladyfinger into the cooled berry sauce (about 1 second per side) and arrange in a single snug layer, breaking cookies as needed to fill gaps.

Spread half the remaining mascarpone cream over the ladyfingers. Scatter the remaining 4 ounces of mixed berries (not the topping berries) evenly over the cream, pressing them in slightly.

Repeat with another layer of sauce-dipped ladyfingers, then spread the remaining mascarpone cream smoothly over the top. Cover tightly with plastic wrap and refrigerate for at least 4 hours or overnight.

Just before serving, arrange the fresh topping berries over the surface. Slice with a sharp knife, wiping clean between cuts for neat slices.