Preheat oven to 350. Line a 9 x 5 x 3 inch loaf pan with parchment paper, then butter and flour the parchment paper.
In the bowl of a stand mixer, whisk the flour, sugar and salt. Whisk in the lemon rind, and poppy seeds. Add butter and ⅓ of the beaten eggs and vanilla to the flour mixture and mix on low until combined, then turn up the speed to medium and beat for a minute. Add ⅓ of the egg mixture and beat until combined then add the last of the eggs and beat until well combined. The batter will be thick.
Pour the batter into the prepared pan and bake for 65-70 minutes, until a toothpick inserted in the center comes out clean. The center will puff up slightly.
While the cake is baking, make the syrup. Cook the sugar and lemon juice in a small saucepan over medium heat until the sugar has dissolved and the liquid is clear.
When the cake is done, remove it and poke holes all over the top with a toothpick. While the cake is still hot, gradually pour the syrup over the top brushing it into the holes and down the sides. Let it cool in the pan for 10 minutes then remove to a wire rack to cool.
Once cooled, wrap it in plastic wrap and let it sit on the counter for a day before slicing. Store at room temperature for 3-4 days or freeze it.