Make the cake: Preheat oven to 350 degrees. Generously brush an 8-inch Bundt pan with oil and dust with flour, tapping out excess.
In a medium bowl, mix together flours, baking powder, and salt. In a large bowl, whisk together sugar and eggs until combined. Add oil, yogurt, lemon zest, and vanilla seeds. Add dry ingredients into wet ones and mix until just barely incorporated. Pour batter into prepared pan.
Bake until golden brown and a tester inserted in the center comes out clean, about 45 minutes. Let cake cool completely in pan before unmolding.
Make the topping: In a small saucepan, bring cane sugar and 1/2 cup water to a boil. Add lemon slices and gently simmer until rind is transparent, 5 to 7 minutes. Remove from heat, drain, and let cool.
In a small bowl, whisk together confectioners' sugar, oil, yogurt, and 2 teaspoons water until smooth. If too thick, adjust with a little more water.
Spoon topping over cake and top with drained lemon slices.