Preheat the oven to 350℉ (175℃). Butter a springform pan (or a cake pan) and line the bottom with parchment paper.
In the bowl of your stand mixer (or a normal mixing bowl, if using a hand mixer), add the sugar and the lemon zest and mix with the whisk attachment until the sugar is the texture of wet sand.
Add eggs, olive oil, Greek yogurt, milk, vanilla, and lemon juice and mix until homogenous.
Over the wed mixture add the flour, salt, baking powder, and soda. Mix on low speed just until incorporated.
Pour the batter into the buttered springform pan lined with parchment paper on the bottom.
Sprinkle 1/4 cup sugar over the top of the olive oil cake in a thin layer.
Bake at 350℉ (175℃) for 50 min or until a toothpick inserted in the middle of the cake comes out clean.