Sift the powdered sugar, almond flour, and raspberry powder together into a bowl. Make absolutely sure there are no lumps, as you want it to incorporate into the egg whites as easily as possible!
Start whipping the egg whites on high speed in the bowl of a stand mixer until they are glossy and hold soft peaks (the stage where the whites will form a peak that droops a few seconds after you pull the whisk out of them). Watch them carefully, as this stage can happen quickly.
Once the eggs have reached the soft peak stage, gently fold the dry ingredients into them. Don't overmix or undermix the batter; instead, fold about 30 turns of the spatula. until the dry ingredients are completely incorporated and the mixture is still stiff enough to pipe.
On a baking sheet lined with a silicone mat, pipe 24 even discs of batter. They should be relatively flat, but not spread uncontrollably. Leave them to sit on the counter at room temperature for an hour, or until a skin forms on the top of the shells. It should be smooth to the touch, and no longer tacky.
Heat your oven to 285 degrees F. Bake the macarons for 12-18 minutes, or until the shells have puffed well and dried out a bit. Once they leave the oven, let them cool for an hour to set up. If you try to remove them from the mat while warm, they will almost definitely crack.
As the shells cool, beat the butter for 2 minutes on medium speed in the bowl of a stand mixer, until creamy. Add the powdered sugar and beat again until incorporated. Add the lemon zest and juice and beat one more time to combine. Once your cookies are cooled and the buttercream is made, pipe a small amount of icing onto half of the cookies and sandwich them together with an uniced cookie.