Preheat oven to 350°F (175°C) and line two baking sheets with parchment paper or silicone mats. Make sure butter and egg are at room temperature before starting.
Zest washed lemons using a Microplane, grating only the bright yellow outer layer to yield 1 tablespoon of zest. Cut lemons in half, juice them, and strain out any seeds to get 2 tablespoons of fresh lemon juice.
While still frozen, roughly chop the raspberries into halves or thirds on a cutting board. Return to the freezer until ready to fold into the dough.
Beat the softened butter, sugar, and lemon zest together on medium speed for 3–4 minutes until light, fluffy, and pale in color. Scrape down the bowl as needed.
Add the egg on low speed until incorporated, then mix in the vanilla extract and fresh lemon juice. Scrape down the bowl — the mixture may look slightly curdled, which is normal.
In a separate bowl, whisk together the flour, baking powder, baking soda, and salt until evenly combined.
With the mixer on low, add the dry ingredients to the wet in three additions, mixing just until no flour streaks remain. Do not overmix — the dough will be thick and slightly sticky.
Take the frozen raspberries straight from the freezer and gently fold them into the dough with a rubber spatula using just a few strokes, leaving beautiful pink and red streaks throughout.
Use a 2-tablespoon cookie scoop to drop dough onto prepared baking sheets, spacing cookies about 2 inches apart — you should get about 12 per sheet.
Bake one sheet at a time for 12–14 minutes, until edges are just lightly golden but centers still look slightly underdone. Keep remaining dough refrigerated between batches.
Let cookies cool on the baking sheet for 5–10 minutes to firm up, then transfer to a wire rack to cool completely before serving.