Preheat the oven to 350 degrees
Mix together the flour, baking soda, sugar, and pudding mix in a large bowl.
In a medium bowl, whisk together the eggs, butter, lemon zest, lemon juice and vanilla together.
Gently fold the wet ingredients into the dry ingredients, until just combined.
Pour into a well greased loaf pan and bake for 35 to 40 minutes or until the top is golden brown and a toothpick inserted in the middle comes out with just a crumb or two.