Preheat oven to 350F and spray an 8x4" loaf pan with baking spray (such as Baker's Joy), or grease and flour the pan.
In a mixing bowl or the bowl of a stand mixer, combine sugar and lemon zest. Use your fingers to mix together, until consistency is similar to wet sand.
Add sour cream, lemon juice, eggs, and oil. Mix on low speed until incorporated.
In a separate small mixing bowl, whisk together flour, baking powder, baking soda, and salt.
With the mixer on low speed, gradually add the dry ingredients, mixing until just combined.
Pour about 2/3 of the batter into the prepared loaf pan. Add half of the lemon curd (1/4 cup) in dollops over the batter. Then add the remaining batter to the pan, followed by dollops of the remaining 1/4 cup of lemon curd.
Use a knife to gently swirl the lemon curd throughout the batter.
Bake for about 50-55 minutes, or until a toothpick inserted in the center of the loaf comes out clean.
Let cool in the pan for about 15 minutes, then run a knife along the edges of the pan to loosen the cake. Remove loaf cake to a cutting board or serving plate.
Prepare glaze by whisking powdered sugar and lemon juice together in a small bowl. Drizzle or brush the glaze over the cake, then let cool completely before serving.