Preheat the oven to 350°F. Have an angel food or tube pan, ungreased, ready for the batter.
Use a rasp grater to finely zest both lemons. Combine the lemon zest and 1 tablespoon fresh or dried lavender flowers with half the sugar in the bowl of a food processor. Process for 10-15 seconds to grind the lavender and mix the ingredients. Add 4 ½ oz cake flour and ¼ teaspoon salt and pulse 3-4x to evenly distribute the ingredients. Remove the blade and set the bowl aside.
In a large mixer bowl or in the bowl of a stand mixer, whisk12 large egg whites on medium speed (#6-7) until very frothy. Combine 1 oz fresh lemon juice and 1 oz water. With the mixer running add the liquid in a slow stream. Continue whipping until soft peaks form. With the mixer running, gradually add the remaining sugar. Increase the speed to medium-high (#7-8) and continue whipping until stiff peaks are formed. The total whipping time will be about 8-10 minutes.
Sift 1/3 of the flour mixture over the meringue and use a whisk to fold in the flour until it's almost incorporated. Sift and fold in the remaining flour mixture in two batches. Fold just until all the flour is incorporated. The batter will still be quite fluffy.
Scoop the batter into the tube pan and spread to even layer. Rap the pan on the counter a couple of times to dislodge any large air bubbles. Bake until the cake is lightly browned, springs back when pressed and a toothpick inserted in the center comes out clean, about 30-35 minutes.
Remove the pan from the oven and immediately invert the pan over a cooling rack. Leave the pan inverted until the cake is completely cool.
Run a small spatula or paring knife around the sides of the cake to loosen and release the cake from the pan.
The cake will keep, well-wrapped, at room temperature for several days.