Position a rack in the lower third of the oven and heat the oven to 350°F.
In a small bowl, whisk 3/4 cup of the sugar, the flour, and salt until evenly combined. Sift the remaining 3/4 cup sugar onto a piece of waxed paper.
In the bowl of a stand mixer fitted with the whisk attachment, beat the egg whites on medium-low speed until frothy, about 1 minute. Turn off the mixer and add the lemon juice and cream of tartar. Increase the speed to medium high and beat until soft peaks form, 2 to 3 minutes. Gradually beat in the sifted sugar and continue beating on medium-high speed until very stiff peaks form, 1 to 2 minutes. Beat in the vanilla.
One-quarter at a time, sift the flour mixture over the whites and, with a large balloon whisk, fold it in quickly but gently. It’s not necessary to incorporate every speck until the last addition of the flour.
Using an offset spatula, spread a thin layer of the cake batter onto the sides of a 10-inch (16-cup) 2-piece metal tube pan. (This ensures smooth sides.) Pour the remaining batter into the pan. Run a knife through the batter to eliminate air bubbles and smooth the surface.
Bake until golden-brown, a wire cake tester inserted in the center comes out clean, and the cake springs back when lightly pressed, 30 to 40 minutes. (A wooden skewer will still have a few moist crumbs clinging to it.) During baking, the center will rise about 2 inches above the pan but will sink to almost level with the pan when done. The surface will have deep cracks, like a soufflé.
Immediately invert the cake: If your pan has feet, simply invert it onto the feet. Otherwise, invert the pan onto a long-necked soda or wine bottle, or a large inverted metal funnel that fits into the tube opening to suspend it well above the counter (if using a soda or wine bottle, fill it with sugar, salt, or marbles to keep it from tipping). Cool the cake completely in the pan, about 1-1/2 hours.
Loosen the sides of the cake with a long metal spatula and remove the cake (still on the tube section) from the sides of the pan. Loosen the cake from the bottom and tube with the spatula or a thin, sharp knife. (A wire cake tester works well around the tube. To keep the sides attractive, press the spatula firmly against the sides of the pan, moving the spatula up and down as you go around.) Invert the cake onto a flat plate or work surface covered with plastic wrap.