Preheat the oven to 350˚F. Grease two 8x4 loaf pans. Lining the bottom of the pans with parchment paper will bring the best result. Set them aside.
Shift flour and baking soda in a bowl and set aside.
In a mixer, beat butter and sugar until soft and creamy, about 2-3 minutes, on medium speed.
Add eggs, on at a time, and beat well until very fluffy.
Add the pudding mix, yogurt, lemon zest, lemon extract, and vanilla extract; beat well.
Add the flour mixture and stir well. Divide the batter into the two prepared loaf pans, smooth out the top. Bake for 55-60 minutes or until the toothpick comes out clean when tested.
Cool in a pan on a rack for 5 minutes then turn the cakes out of the pan and let them cool completely.
For the icing, mix powdered sugar, lemon juice, and milk. You can add a couple drops of lemon extract if you prefer more citrus flavor. Drizzle over the cooled cakes.