Place 1 cup sliced strawberries with 1 tablespoon sugar in a bowl and let sit 15–20 minutes to macerate; strain and reserve about 2 tablespoons of juice for the glaze, then lightly mash half of the macerated berries and chop the rest.

Preheat oven to 325°F and grease and flour a 9×5-inch loaf pan or line with parchment.

Cream 1 cup butter with 1 1/2 cups sugar until pale and fluffy, about 3–4 minutes; add eggs one at a time, mixing well after each addition, then stir in 1 teaspoon vanilla and 1/2 teaspoon lemon zest.

Whisk together 2 1/4 cups flour, 1/2 teaspoon baking powder, and 1/2 teaspoon salt in a separate bowl; whisk 1/2 cup sour cream with 1/4 cup milk in another measuring cup.

Add dry ingredients to the butter mixture in three parts, alternating with the sour cream mixture and beginning and ending with the dry ingredients; mix just until combined.

Fold in the chopped and mashed macerated strawberries gently, then transfer the batter to the prepared loaf pan and smooth the top.

Bake at 325°F for 55–65 minutes, or until a toothpick inserted into the center comes out with a few moist crumbs; tent with foil if the top browns too quickly.

Cool the pan on a wire rack for 15 minutes, then remove the cake from the pan and cool completely on the rack, about 45 minutes.

Whisk 1 cup powdered sugar with 2 tablespoons reserved strawberry juice and 1–2 teaspoons milk until smooth and pourable; drizzle over the cooled loaf and let set for 15–20 minutes before slicing.