Heat the oven to 350°F. Grease and lightly flour two 9×5-inch loaf pans. Set aside.

In medium bowl, sift or whisk together the flour, baking powder, and salt; set aside.

In a large bowl or the bowl of a stand mixer fitted with the paddle attachment, cream together the sugar and butter until light and fluffy. Add the lime juice, lime zest, and eggs, beating on high speed for 2-3 minutes.

Add the flour mixture into the sugar mixture alternately with milk on low speed, beating just until smooth after each addition.

Pour the batter evenly into the prepared pans.

Bake the cakes on the middle rack for 55 to 60 minutes, or until a toothpick inserted in center comes out clean. Cool for 20 minutes; remove from pans to wire rack. Cool completely, about 2 hours.

When the cakes are cooled, make the glaze by whisking together powdered sugar, 2 tablespoons milk, and lime zest. Add more milk very sparingly until a drizzle-able consistency is achieved.

Place the cake on a cooling rack with aluminum foil or parchment underneath. Spoon the glaze over cakes and let excess drip below. Let glaze set and then transfer to serving tray.