Preheat oven to 350F. Line a 9×9-inch baking pan with aluminum foil and grease lightly.
In a large bowl, cream together butter and brown sugar until fluffy. Add in flour, baking powder and salt and mix until everything comes together in a crumbly mixture and flour is evenly distributed.
Mix in oats and coconut. Mixture will be somewhat dry and sandy.
In a medium bowl, whisk together sweetened condensed milk, lime juice and lime zest.
Put 2 cups of the oat mixture into the bottom of prepared baking dish and press firmly into an even layer. Pour lime mixture on top and spread evenly. Crumble all remaining oat mixture over the top of the lime mixture, covering it completely.
Bake for 30-35 minutes, until golden brown.
Cool completely on a wire rack before cutting into squares.