Preheat the oven to 350°F (177°C). Line 18 standard muffin cups with paper liners.
In the bowl of a stand mixer, gently stir or toss the butter and granulated sugar until the butter is coated. Attach the bowl and paddle to the mixer and beat the butter and sugar on medium speed until a paste forms and there are no visible clumps of butter, about 5 minutes.
In a small bowl, whisk together the sour cream, eggs, vanilla, and lemon juice. Reduce the mixer speed to low and slowly drizzle in the egg mixture. With a rubber spatula, scrape down the sides of the bowl.
In a separate bowl, sift the flour, baking powder, baking soda, cinnamon, nutmeg, and salt together. With the mixer on low speed, gradually add the dry ingredients to the butter and mix until just incorporated.
Cut the apples away from the core in 4 sections. Place a box grater over a plate and, holding the apples by the peel side, grate the apples against the large side of the grater until you're left with just the peel. Discard or compost the peels.
Immediately fold the grated apples into the batter.