1. Preheat oven to 350 degrees F. Grease a 8×8-inch baking pan and set aside.
2. In a large bowl, cream together butter and brown sugar. 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.
3. In a medium bowl, whisk together sweetened condensed milk, vanilla, lime juice, and lime zest.
4. 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.
5. Bake bars for 30-35 minutes, or until golden brown. Cool completely on a wire rack. Cut into squares and serve. Store remaining bars in the refrigerator.