Hull and slice the berries into even ¼-inch pieces. Toss with 2 tablespoons granulated sugar in a bowl. Let sit 10 minutes so juices release.
Beat softened cream cheese with powdered sugar, vanilla, and lemon juice until smooth and fluffy, about 2 minutes. In a separate bowl, whip the cold heavy cream to stiff peaks. Gently fold the whipped cream into the cream-cheese mixture until no streaks remain. The filling should look thick and cloud-like.
Spread a thin layer of cream on the bottom of a 9×13-inch dish. This keeps the first crackers from sliding. Arrange a single layer of graham crackers over the cream, breaking pieces as needed to fit.
Spread one-third of the remaining cream over the crackers. Spoon one-third of the sugared strawberries (plus some juices) evenly on top.
Add another layer of graham crackers, then cream, then strawberries. Repeat once more so you finish with a cream layer on top. Press gently so everything sits flat.
Cover the dish tightly with plastic wrap. Refrigerate at least 4 hours, preferably 6 hours or overnight. The crackers will soften into cake texture and the cream will set for clean slices.
Just before serving, top with remaining fresh strawberry slices and a light dusting of powdered sugar if desired. Slice into squares with a sharp knife wiped clean between cuts.