Preheat oven to 200 degrees.
Line two baking sheets with parchment paper and trace two circles, 8-inches in diameter, on each piece of parchment paper, four circles altogether between the two pans.
In the bowl of a standing mixer with the whisk attachment, beat the egg whites and lime juice on medium speed until frothy, about 3 to 4 minutes. Continue beating and start adding the granulated sugar slowly, about 2 tablespoons at a time, until completely combined and the mixture holds stiff peaks, about 2 to 3 more minutes. The meringue should appear white and glossy.
Remove the bowl from the stand, sift the cornstarch into the meringue, and use a rubber spatula to gently fold and completely incorporate the cornstarch. Transfer the meringue to the prepared baking sheets, dividing evenly between the 4 8-inch measured circles. Use the spatula to spread it into even circles; you will be able to make some nice wavy shapes.
Bake for 1 hour, then reduce the temperature to 175 degrees. Let the meringue dry in the oven for another 4 to 6 hours. The outside should be crisp, and they should be easy to remove from the parchment. Set aside to cool completely.
In the bowl of a standing mixer with the whisk attachment, whip the heavy cream and mascarpone cheese until soft peaks form. Add the vanilla and continue to beat until stiff peaks form.
Transfer 1 1/4 cups of the whipped mascarpone cream to a medium bowl and fold in the sliced strawberries. Set aside.
To assemble the cake, place a round of meringue on platter and spoon about 1 1/4 cup whipped cream onto the center, then spread to cover. Top with the second meringue and spread on the strawberry and whipped cream mixture. Top with the third meringue and another 1 1/4 cup whipped cream. Top with the final meringue. Serve in slices with more fresh strawberries.