Preheat oven to 325°F (160°C). Grease and flour a 10-inch bundt or loaf pan, or line a loaf pan with parchment.
Beat butter and sugar until pale and fluffy, about 3–5 minutes in a stand mixer or with a hand mixer.
Add eggs one at a time, beating briefly after each addition and scraping down the bowl as needed.
Mix in sour cream, milk, lemon zest, and lemon juice until combined.
Whisk flour, baking powder, baking soda, and salt. Add to wet ingredients in two additions, mixing on low until just combined.
Fold in 1 cup blueberries. Toss remaining 1/2 cup with a teaspoon of flour; reserve to layer and lightly swirl into batter once in the pan.
Bake for 55–70 minutes until a toothpick inserted in the center comes out with a few moist crumbs. Tent with foil if browning too quickly.
Cool in the pan 15 minutes, invert onto a rack to cool completely. Whisk powdered sugar with lemon juice to a pourable consistency, drizzle over the cooled cake, and let set.