Preheat oven to 175 °Celsius.
Beat butter and sugar till light and fluffy for about 2 minutes. Add eggs, one at a time, beating well after each addition.
In a separate bowl, sift flour, baking powder, and salt. Fold in the sifted ingredients into the creamed mixture alternately with milk and lime juice. Start and end with flour.
Finally, fold in the grated lime rind.
Pour the cake batter into a well-greased and floured loaf cake tin. Level the top.
Bake the lime pound cake for 40 to 45 minutes until a skewer inserted in the center of the cake comes out without any wet batter.
Remove the cake from the oven and let it cool in the tin for 4 to 5 minutes before turning it out onto a wire rack to cool further.
To make the lime sugar glaze, sift the powdered sugar into a small bowl.
Add the warm water and lime juice and mix until smooth.
Transfer the glaze into a piping bag.
Make a small snip at the tip of the icing bag and drizzle the glaze onto the cake generously.