Preheat oven to 350°F. Grease and flour a 9x5-inch loaf pan. Optional: line the pan with parchment paper extending over the sides of the pan to allow for easy removal.
In a bowl, whisk together flour and baking powder.
In the bowl of a stand mixer or in a large bowl using a hand mixer, cream butter and sugar on medium speed for 5 minutes until light in color and fluffy.
Add the eggs one at a time, mixing fully before adding the next.
Add lime zest and mix to incorporate.
In a small bowl, mix condensed milk and lime juice together. Add to mixer bowl and beat until smooth.
Gently fold in dry ingredients using a rubber spatula until just barely combined.
Pour batter into prepared pan until it is just ¾-inch from the top. Drop the pan once from 2 inches above the countertop to eliminate air pockets.
Bake for 55-65 minutes, or until a toothpick inserted into the center of the loaf comes out clean. Cool in pan for 10 minutes and then transfer to a wire rack to cool completely.
For icing, whisk together all the glaze ingredients until smooth. Add more lime juice if needed for thinner consistency. Pour over cooled cake.
Notes
Glaze: Because of the sweetened condensed milk in the glaze, it does not set completely. I find that the condensed milk gives it that distinctive key lime pie flavor, but if you prefer a glaze that sets, you can omit the condensed milk in the glaze and adjust your lime juice accordingly.