Preheat oven to 350F. Line a 12-cup muffin tin with paper liners. In a large bowl, whisk together flour, sugar, baking powder, and salt. Add the softened butter and beat with an electric mixer on low until the mixture looks like damp sand with no visible butter chunks, about 2 minutes.

Beat in the eggs one at a time, mixing until fully incorporated after each. Add the milk, lemon zest, and lemon juice. Beat on medium speed for 2 minutes until the batter is smooth, light, and slightly fluffy. Scrape down the bowl halfway through.

Gently fold in the raspberries with a rubber spatula, taking care not to crush them. The batter will look slightly streaked with pink - this is fine. Divide evenly among the liners, filling each about two-thirds full.

Bake for 18-20 minutes, rotating the pan halfway through, until the tops spring back when lightly touched and a toothpick inserted in the center comes out clean. Let cool in the pan for 5 minutes, then transfer to a wire rack to cool completely before frosting.

In a large bowl, beat the softened butter on medium-high speed until creamy and pale, about 3 minutes. Gradually add the powdered sugar on low speed, then increase to medium and beat until fluffy, about 2 minutes.

Add the lemon juice, lemon zest, and salt. Beat on medium-high for 2-3 minutes until the frosting is light, fluffy, and spreadable. If too thick, add a teaspoon of milk; if too thin, add a tablespoon of powdered sugar. Frost cooled cupcakes with a knife or piping bag.