Heat oven to 350 degrees. Grease and lightly flour two 9×5-inch loaf pans.
In medium bowl, sift together flour, baking powder and salt; set aside.
In a large bowl or the bowl of a stand mixer fitted with the paddle attachment, beat sugar and butter until light and fluffy. Add lime juice and eggs, beating on high speed for 2-3 minutes.
Add flour mixture into sugar mixture alternately with milk on low speed, beating just until smooth after each addition.
Fold in lime zest.
Pour into prepared pans.
Bake 55 to 60 minutes, or until toothpick inserted in center comes out clean. Cool 20 minutes; remove from pan(s) to wire rack. Cool completely, about 2 hours.
When cakes are cooled, make glaze.
Whisk together powdered sugar, milk and lime zest. Add milk very sparingly until a drizzle-able consistency.
Place cake on cooling rack with aluminum foil or parchment underneath. Spoon glaze over cakes and let excess drip below. Let glaze set and then transfer to serving tray.
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