Make the Strawberry Filling: In a saucepan over medium heat, combine the quartered strawberries, sugar, and lemon juice. Cook for 8–10 minutes, stirring occasionally, until the strawberries break down and the mixture thickens slightly. Let it cool completely.
Prepare the Mascarpone Filling: Beat the mascarpone cheese, powdered sugar, lemon juice, and vanilla extract until smooth and creamy. Set aside.
Mix the strawberry milk and syrup in a shallow bowl.
Quickly dip each ladyfinger into the mixture, just long enough to soak slightly without getting soggy.
Arrange half of the dipped ladyfingers in the bottom of the baking dish.
Spread half of the mascarpone filling evenly over the ladyfingers.
Spoon the cooled strawberry filling on top.
Add another layer of dipped ladyfingers.
Spread the remaining mascarpone filling evenly over the top.
Cover and refrigerate for at least 30 minutes (or up to 4 hours) so the flavors meld.
Just before serving, sprinkle the strawberry dust evenly over the top.
Garnish the edges with fresh strawberry slices if you like.