Preheat the oven to 350°F (175°C). Grease two 9×5-inch loaf pans and lightly dust with flour.

In a medium bowl, whisk together flour, baking powder, and salt.

In a large bowl, cream sugar and butter until light and fluffy. Add eggs one at a time, mixing well after each addition. Stir in lime juice and zest.

Gradually add dry ingredients to the creamed mixture alternately with milk, beginning and ending with the flour mixture. Mix until just combined.

Pour batter into prepared pans, filling them about two-thirds full. Gently tap pans to release air bubbles.

Bake for approximately 55 minutes or until a toothpick inserted comes out clean. Cool in pans for 20 minutes before transferring to wire racks.

For the glaze, mix powdered sugar with milk until smooth; drizzle over cooled cakes.