Heat oven to 350°F. Grease a 9x5-inch loaf pan and lightly flour it.
Hull and finely chop strawberries. Pat dry, then toss with 1 tbsp flour; set aside.
Cream softened butter and sugar on medium speed until pale and fluffy, about 3–4 minutes.
Beat in eggs one at a time, mixing well and scraping the bowl after each. Stir in vanilla and lemon zest.
Whisk flour, baking powder, and salt in a bowl. On low speed, add half the dry mix, then all sour cream, then remaining dry mix; mix just to combine.
Fold floured strawberries into the batter gently to avoid streaking.
Spread batter into the prepared pan and smooth the top. Tap the pan once to release air.
Bake 55–65 minutes, until a toothpick comes out clean. Tent with foil if browning early.
Cool in pan 15 minutes, then turn out to a rack and cool completely.
Whisk powdered sugar, strawberry puree, and lemon juice. Thin with a splash of milk to a thick drizzle.
Drizzle glaze over the cooled cake. Let set 10 minutes before slicing.