For the cake, place oven rack to the lower-middle position and preheat oven to 325º F. Wipe clean a large tube pan (16 cup capacity) with removable bottom. Do not grease!
Combine flour and 3/4 cups of the sugar in a small bowl, whisking well. Set aside.
Beat egg whites in the bowl of a standing electric mixer at low speed until the eggs are beginning to froth. Add cream of tartar and salt. Increase speed to medium and beat until whites form soft, billowy, slightly translucent mounds. Keeping the mixer on medium-speed, add remaining 3/4 cup sugar one tablespoon at a time.
Continue beating on medium speed until the whites form soft glossy peaks that bend over at the points. Resist the temptation to increase mixer speed, and take care not to over-beat; the batter should still flow when the bowl is tilted.
Add vanilla and lemon juice and beat until just blended.
Sift a fine layer of the flour-sugar mixture over the whites (no more than 3 tablespoons at a time) and fold it in gently using a large silicone spatula. Repeat with remaining flour-sugar mixture.
Scrape the batter into the ungreased pan, smooth the top, and tap the pan on the counter two times to release any large air bubbles.
Bake until the cake is golden brown and the top springs back when pressed firmly, about 50 to 60 minutes. Let the cake cool upside down for 2 to 3 hours; invert the pan on a wine bottle if the pan does not have prongs around the rim.
To unmold the cake, slide a thin knife or spatula around the inside edge of the pan, pressing firmly against the pan to avoid tearing the cake. Slide the cake from the pan and run the knife under the cake on the removable bottom in the same way to detach it. Place cake bottom-side up on a platter.
To prepare the frosting, cream butter in the bowl of a standing electric mixer with the paddle attachment.
When the butter is light and fluffy, turn off the mixer and add powdered sugar, cocoa powder, salt, vanilla, and milk to the bowl.
Stir to combine on low speed until the mixture comes together. Increase mixer speed to medium and beat for about 3 minutes.
Adjust the consistency with more powdered sugar or milk as needed.
Frost cake and serve!