Preheat oven to 3750 Mix and whisk first 5 ingredients in a medium bowl.
Mix room temp. butter and sugars together until creamy and fluffy with an electric mixer. Add eggs one at a time to butter mixture and then vanilla, lime juice and lime zest.
Mix dry flour mixture into wet butter mixture, reducing mixer speed until all combined. Stir in both kinds of chocolate chips.
Drop by spoonfuls on a parchment covered baking sheet (or use spray oil). I cooked 12 on a sheet. Bake for 8-12 minutes or until edges are light brown.
Cool on a wire rack. While cooling mix confectioner sugar, lime juice and zest together to form a thin glaze. When cookies are cool drizzle with a spoon onto top of cookie.