Preheat your oven to 350°F (175°C) and grease an 8-inch round cake pan, lining it with parchment paper. Bring all refrigerated ingredients to room temperature.
In a medium bowl, whisk together flour, baking powder, baking soda, and salt. Set aside.
In a large bowl, beat softened butter and granulated sugar with an electric mixer until light and fluffy, about 3-4 minutes.
Add eggs one at a time, beating well after each addition. Scrape the sides of the bowl and mix in vanilla extract and lemon zest until combined.
Alternate adding the dry ingredients and buttermilk-lemon juice mixture, starting and ending with the flour mixture. Mix on low speed to avoid overmixing.
Gently fold in chopped strawberries with a spatula until evenly distributed.
Pour the batter into the prepared pan, smooth the top, and bake for 30-35 minutes, or until a toothpick inserted comes out clean.
Let the cake cool in the pan for 10 minutes, then invert onto a wire rack to cool completely.
For the glaze, whisk together powdered sugar, lemon juice, and strawberry puree until smooth. Adjust the consistency with more sugar or juice as needed.
Once the cake has cooled, drizzle the glaze over the top, letting it drip down the sides.