Preheat oven to 325°F (160°C). Grease and flour a 9x5-inch loaf pan.
In a medium bowl, whisk together the flour, sugar, salt, and baking powder.
In a separate large bowl, cream together the butter and sugar until light and fluffy.
Beat in the eggs one at a time, then stir in the lemon zest and vanilla extract.
Gradually add the dry ingredients to the wet ingredients, alternating with the lemon juice, beginning and ending with the dry ingredients. Mix until just combined.
Pour the batter into the prepared loaf pan and spread evenly.
Bake for 65-75 minutes, or until a wooden skewer inserted into the center comes out clean.
Let the cake cool in the pan for 10 minutes before inverting it onto a wire rack to cool completely.