Preheat oven 350F, with rack on lower middle position. Lightly grease 9x5" loaf pan and set aside.
In a bowl, hand-whisk together the yogurt, sugar, eggs, lemon zest, vanilla, and olive oil. Whisk until well incorporated.
In a separate bowl, hand-whisk together the flour, baking powder, and salt. Using a rubber spatula or wooden spoon, gently fold flour mixture together with the yogurt mixture until most lumps are gone (a few small lumps are fine.) Scrape batter into greased loaf pan and bake 60-70 min or until toothpick inserted in center comes out almost clean, with a few tender crumbs attached.
Allow cake to cool slightly at room temp, while you make the lemon syrup. Combine the 2 ingredients for Lemon Syrup into a saucepan. Stir over medium heat until completely dissolved. Use a sharp knife to loosen warm cake from pan and carefully flip cake over onto a serving platter. Using a bamboo skewer or toothpick, poke holes throughout top of cake. Evenly distribute lemon syrup over the cake (I use my pastry brush) until it's all soaked into the cake. Let cake cool at room temp.
When cake is mostly cool, make the lemon glaze by combining the 3 ingredients for Lemon Glaze in a small bowl and stirring until it becomes a thick yet drizzly consistency. Drizzle glaze over cooled cake. Allow glaze to firm up, about 5 min. Slice and serve.
Notes
This cake is delicious as leftovers. Keep in an airtight container at room temp 1-2 days. It can also be frozen, in airtight container, for several weeks.