Preheat oven to 350 degrees Fahrenheit. Butter and flour a large bundt pan.
Sift flour, baking powder, and salt into medium bowl. Set aside.
Using an electric mixer, cream together butter, coconut oil, and sugar. Add eggs one at a time, mixing well with each addition.
Alternate adding the dry ingredients and milk to the butter mixture. Starting and ending with dry ingredients, and mixing until just incorporated between each addition. (Add ⅓ of the dry ingredients to the butter mixture. Mix. Add ½ the milk. Mix. Add another ⅓ of the dry ingredients. Mix. Add the rest of the milk. Mix. Add the rest of the flour. Mix until just incorporated.)
Mix in lime juice and zest until just incorporated.
Pour batter into prepared bundt pan. Spread evenly with a spatula. Bake at 350 degrees Fahrenheit until a toothpick inserted into the thickest part of the cake comes out clean, about 45 to 55 minutes. Cool cake in pan for 10 minutes. Turn cake out onto a plate and cool completely.
Make the glaze by whisking the ingredients together to desired consistency, adding more lime juice to thin, or more powdered sugar to thicken. Pour over cooled cake. Slice and serve. Store cake in an air tight container up to 5 days.