Preheat oven to 325°. Spray a 9-in. springform pan with cooking-oil spray and reserve. Pour 2 in. water into a medium saucepan and bring to a boil; reduce heat to a simmer. Put 4 eggs, 1/2 cup sugar, and the vanilla in the bowl of a stand mixer. Set bowl over simmering water, making sure bottom doesn't touch the water, and whisk egg mixture constantly just until the sugar is dissolved and mixture is no longer cool to the touch, 2 to 3 minutes.
Add 2 tbsp. lemon zest to egg mixture and whip on high speed with whisk attachment until batter is pale in color, has thickened considerably, and drops in ribbons when whisk is lifted, 7 to 8 minutes.
Sift flour over egg mixture in several batches, folding after each batch just to incorporate. Add butter in 2 batches, folding just until incorporated.
Pour batter gently into prepared pan. Bake until cake is cooked through and a toothpick inserted into center comes out clean, 26 to 28 minutes. Let cool completely on a wire rack, then remove sides of pan.
Meanwhile, line a metal mixing bowl (9- to 10-in. diameter) with enough plastic wrap to hang over rim. Chill in freezer 15 minutes. Put strawberry ice cream in cleaned bowl of stand mixer (now fitted with a paddle attachment) and beat on medium speed until ice cream is smooth and malleable (like taffy), about 1 minute. Using a rubber spatula, spread ice cream into chilled bowl, smoothing surface as flat as possible, and return to freezer.
Put vanilla ice cream, lemon juice, and remaining 3 tbsp. lemon zest in cleaned bowl of stand mixer and beat on medium speed until smooth and malleable (like taffy), about 1 minute. Spread over strawberry ice cream. Press cake on top of lemon ice cream, trimming to fit if needed. Fold edges of plastic wrap over cake. Cover with more plastic wrap and freeze at least 6 hours and preferably overnight.
Preheat oven to 475°. Put egg whites and cream of tartar in cleaned, dry bowl of stand mixer fitted with a whisk attachment; beat on high speed until whites are foamy, about 1 minute. Add remaining 1 cup sugar and continue to beat until whites are stiff and glossy, 2 to 3 minutes.
Remove cake and ice cream from freezer and take off top layer of plastic wrap. Carefully dislodge ice cream layers from sides of bowl by pulling up on plastic-wrap liner. Invert bowl onto an ovenproof plate and peel off outer layer of plastic. Using an offset spatula, mound meringue on top of ice cream and then work downward, spreading meringue evenly over top and sides of cake and ice cream. Bake until meringue is browned and toasty, 6 to 7 minutes. Serve immediately.