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Preheat oven to 350°. Coat loaf pan with vegetable oil spray. Dust with flour; tap out excess.
Whisk 1 1/2 cups flour, baking powder, and kosher salt in a medium bowl.
Using your fingers, rub sugar with lemon zest in a large bowl until sugar is moist. Add yogurt, oil, eggs, and vanilla extract; whisk to blend. Fold in dry ingredients just to blend.
Pour batter into prepared pan; smooth top. Bake until top of cake is golden brown and a tester inserted into center comes out clean, 50–55 minutes.
Let cake cool in pan on a wire rack for 15 minutes. Invert onto rack; let cool completely. DO AHEAD: Can be made 3 days ahead. Store airtight at room temperature.