Heat oven to 350 degrees. Butter and flour an 8-inch loaf pan.
In a bowl, combine lemon zest and sugar and rub with your fingers until it looks like wet sand. Whisk in buttermilk, 3 tablespoons lemon juice and the eggs. In a separate bowl, whisk together 1 3/4 c. flour, baking powder, baking soda and salt. Whisk dry ingredients into the batter, then whisk in oil and poppy seeds.
Pour batter into prepared pan. Bake until a toothpick inserted in the center emerges clean, about 1 hour. Let cool in pan until warm to the touch, then turn out onto a baking rack set over a rimmed baking sheet. Turn cake right side up.
Whisk together remaining 4 teaspoons lemon juice and the powdered sugar. Use a pastry brush to spread glaze evenly over top and sides of cake. Cool completely before slicing.