For the cake: Preheat the oven to 350°F. Grease a 9-by-5-inch loaf pan and set aside (see tip).
To a large bowl, add the granulated sugar, eggs, and lemon zest. With a hand mixer or whisk, whip the mixture until light and fluffy, 2 to 3 minutes. Add the oil, Greek yogurt, lemon extract, food coloring, and lemon juice and mix until smooth.
In a separate large bowl, whisk together the flour, baking powder, baking soda, and salt. Fold the flour mixture into the wet ingredients until just combined. Transfer the batter to the prepared loaf pan, smoothing the top with a spoon or small offset spatula.
Bake until golden and a toothpick inserted in the center comes out clean, 50 to 55 minutes.
For the soak: In a small bowl, mix together the lemon juice and powdered sugar. Pour over the cake while it is still hot. Let the cake cool completely in the pan, about 1 hour.
For the glaze: Meanwhile, in a medium bowl, combine the powdered sugar, lemon juice, butter, and 1 tablespoon water. Mix until smooth and easy to drizzle; set aside.
When the cake is cooled, remove it from the pan and place it on a cooling rack. Pour the glaze over the cake, allowing it to drip down all sides. Let sit for 30 minutes to set before slicing and serving.
