Preheat your oven to 350°F (175°C) to ensure even baking.
Grease your loaf pan with softened butter and dust with flour to help the cake release easily.
In a medium bowl, whisk together flour, baking soda, baking powder, and salt. Set aside.
In a large bowl, beat butter and sugar together on medium speed until light and fluffy, about 3-5 minutes.
Add eggs one at a time, mixing well after each. Then mix in vanilla, lemon zest, and lemon juice until combined.
With the mixer on low, alternate adding dry ingredients and milk until all is combined. Mix until smooth without overmixing.
Pour the batter into the prepared loaf pan, smoothing the top with a spatula.
Bake for 60-70 minutes, or until a toothpick comes out clean. Cover with foil if browning too quickly.
Cool in the pan for 10 minutes, then transfer to a cooling rack to cool completely.
In a small bowl, whisk together granulated sugar, lemon juice, powdered sugar, and cream until smooth. Adjust consistency as needed.
Drizzle the glaze over the cooled cake, letting it drip down the sides. Allow to set before slicing.
