Place rack on bottom rung of oven; preheat to 325°F.
Make cake: Using an electric mixer, beat all egg whites at medium speed for 1 minute. Add cream of tartar; beat until stiff, 3 minutes. Sift flour, sugar, baking powder and salt into a bowl. In a separate bowl, whisk together yolks, oil, lemon juice, lemon zest, vanilla and 1/4 cup water. Stir yolk mixture into dry ingredients. Fold 1/3 of egg whites into batter, then fold in remaining whites. Scrape batter into an ungreased 10-inch tube pan.
Bake cake until a tester inserted in center comes out clean, 50 to 55 minutes. Invert pan; let cool.
Make frosting: In a pan, bring sugar and 1/2 cup water to a boil over high heat, stirring to dissolve sugar. Boil until mixture reaches 240°F on a candy thermometer. Using an electric mixer, beat egg whites, salt and cream of tartar at medium speed until stiff but not dry. Beat hot sugar syrup into mixture. Add vanilla; beat until cool.
Run a thin, sharp knife around outside and inside of cake to loosen it from pan. Transfer cake to a platter, frost and serve.