Stir the hot water with the matcha powder until smooth. It will be thick and dark green. Allow to cool while you prepare the rest of the ingredients.
Make superfine sugar.
Pour the granulated sugar into a food process and mince on high for about 15 seconds to make superfine sugar.Remove 3/4 cup of the sugar from the food processor.
Combine dry ingredients.
Whisk together the cake flour and the 3/4 cup of the sugar in a separate bowl and set aside.
Make the meringue.
Preheat the oven to 350 degrees Fahrenheit.In the bowl of a stand mixer with a whisk attachment, add the egg whites and whisk on medium-high until foamy. Add the cream of tartar and continue to whip for a minute until the bubbles begin to tighten. With the mixer running continuously, add the cooled matcha paste, a tablespoon at a time to the egg whites. Wait about 30 seconds between each addition so the meringue doesn't collapse under the weight of the paste.Once the matcha is all in, start adding sugar. Only add about a tablespoon at a time as well for this ingredient and count 20 seconds between each addition. Once all the sugar is all in continue to whip the meringue until it has reached (nearly stiff) soft peaks It will take quite a bit longer than normal for the meringue to be ready because of the matcha paste. It's a very heavy ingredient and you will really need to whip a lot of air into the meringue to support all of that extra weight. I actually let the whites reach close to stiff peaks for this cake. Still soft enough to slightly collapse back on itself but not completely stiff either. The time it takes to reach the appropriate peak will take longer than usual for a meringue also. It took 12 minutes from start to finish for me, so just be patient.In the last minute of whisking, add the lemon zest, vanilla and salt while the mixer is still running.
Add the dry ingredients.
Hold a fine strainer over the bowl of whipped matcha meringue. Add 1/3 of the dry ingredients to the strainer and tap the strainer to evenly dust the top of the meringue. Use a rubber spatula to gently fold the dry ingredient mixture into the meringue. Don't worry about having the first or second additions of the dry fully folded in so as not to risk over mixing and deflating the egg whites. By the time you get to the third addition, you can focus on getting the batter evenly combined.
Bake the cake.
Use the rubber spatula to scoop spoonfuls of the batter evenly into an ungreased tube pan. Be gentle with the batter so it doesn't loose any air. Once it is all in you can take the spatula and very gently even out the top. Place It in the middle rack of the oven bake for 45 minutes. Remove the cake from the oven. Once it is cool enough to handle and turn the pan upside down to finish cooling. Allow to cool completely before removing the cake from the pan. Run a butter knife between the outer edge of the cake and the pan. Do the same thing with the inner tube section. Release the cake from the walls of the pan by pressing on the false bottom. Run the knife between the bottom of the cake and the pan, then slide the cake gently off the center tube. Serve immediately or wrap in plastic wrap and refrigerate for up to 2 days.