Preheat the oven to 325˚F. Spray a 9x5 inch loaf pan with cooking spray and line it with parchment paper. Set it aside for later.
In a medium sized bowl, combine the flour, baking powder, and salt. Whisk until the ingredients are evenly distributed.
In a large bowl, add in the butter and sugar. Cream the butter and sugar together until it becomes light and fluffy. Add in the egg, vanilla extract, and lime zest. Mix until incorporated.
Add in 1/3 of the flour mixture into the bowl and lightly fold it into the batter. When most of the flour has been incorporated, add in half of the coconut milk and half of the lime juice and mix until combined. Add in half of the remaining flour mixture and fold it into the batter. Mix in the remaining coconut milk and lime juice. Then add in the remaining flour, folding it in until combined.
Transfer the batter into the loaf pan. Shake the pan from side to side to get the batter to settle evenly. Place the pan on top of a sheet tray and bake for about 1 hour and 5 minutes. If you insert a toothpick into the center of the bread it should come out clean. Remove the bread from the oven and allow it to cool for 5 minutes. After 5 minutes, remove the bread from the loaf pan and allow it to cool on a wire rack.