Cut frozen cake crosswise into 1/2-inch-thick slices. Line bottom of a 9-inch pie plate with cake slices, some halved or cut into pieces to fill in gaps. Halve remaining cake slices lengthwise and place around edge of plate. Patch up any holes with pieces of remaining cake slices. (You may have a couple of slices left over.)
Cut paper containers from ice cream and slice each pint into 3 rounds. Arrange 3 rounds in 1 layer on top of cake in pie plate and cut each remaining round into 6 wedges. Fill holes in ice cream layer with some of ice cream wedges and mound remainder in center of pie plate. Freeze 25 minutes.
Preheat oven to 450°F.
After ice cream and cake have been freezing 20 minutes, beat egg whites and a pinch of salt with an electric mixer until foamy, then add lemon juice and continue to beat until whites hold soft peaks. Gradually add sugar, beating, and continue beating until whites just hold stiff, glossy peaks.
Remove ice-cream base from freezer and mound meringue over it, spreading to edge of plate to cover ice cream completely.
Bake in middle of oven until golden brown, about 6 minutes.
Serve immediately.
• The base can be assembled 2 days ahead and frozen, tightly wrapped. Make meringue and, after topping base, bake Alaska 10 minutes.• The egg whites in this recipe may not be fully cooked. If salmonella is a problem in your area, you can use powdered egg whites such as Just Whites.
