Preheat the oven to 350°F. Grease a 9-by-5-inch loaf pan with nonstick cooking spray or olive oil.
Combine the yogurt, chia seeds, 2 tablespoons lemon juice, and 1 tablespoon zest in a small bowl and set aside.
In a medium bowl, whisk together the flour, baking soda, and salt.
Using a stand mixer on high speed, beat the olive oil and granulated sugar until combined, about 4 minutes. Stir in the vanilla extract and then add the eggs in one at a time, beating well between each addition, scraping down the sides of the bowl as needed.
Reduce the speed to low, now add the dry ingredients in 3 batches, alternating with 2 batches of the chia yogurt mixture.
Pour batter evenly into prepared pan and smooth the top with an offset spatula. Bake cake in the center of the oven, until a cake tester, comes out clean, and the top has set, about 40 to 45 minutes or internal temperature reaches 205 to 210°F on a thermometer.
If the top begins to brown rapidly towards the final minutes of baking (around 35 minutes), tent the cake loosely with foil, but without touching the surface. Allow to cool in the pan for 10 minutes then carefully remove and transfer to a cooling rack.
Combine the confectioners sugar, 2 tablespoons lemon juice, and ½ teaspoon zest together, adjusting with more lemon juice or powdered sugar until you get a glue-like consistency.
Drizzle the glaze over the cake letting it drip down the sides. Sprinkle with ½ teaspoon lemon zest. Let it set and serve warm or cool.
I find that 3/4 cup white whole wheat flour plus 3/4 cup all-purpose flour gave an even more tender cake. You can make this substitution if you're okay not having all whole wheat flour in the recipe.
You can also replace all of the whole-wheat flour with all-purpose flour.
If you like the taste of poppy seeds, add 1/2 to 1 tablespoon in addition to the chia seeds. You could also substitute the poppy seeds completely for chia seeds.