Preheat the oven to 375F. Line 12 muffin tins with cupcake liners.

Beat together the butter, coconut oil, and the sugar until light and fluffy. Add in the eggs, one at a time, until fully incorporated. Stir in the lemon zest, juice and vanilla extract.

In a large bowl, mix together the flour, baking powder and salt.

Add one third of the dry ingredients to the butter mixture and mix until combined. Add half of the milk and combine, followed by another third of the flour mixture. Add in the remaining milk then the remaining dry ingredients, mixing just until combined.

Divide the mixture evenly between the prepared tins and bake in the preheated oven until a tester inserted in the center comes out clean, about 18 minutes. Cool completely.

While the cupcakes are cooling, start the frosting. Place the pomegranate juice in a small saucepan and bring to a boil. Boil until it has reduced by half. Cool completely.

Beat the butter until light and creamy. Add the powdered sugar and beat on low until combined. Add in the cooled, reduced pomegranate juice and beat until smooth and fluffy, about 3 minutes.

Pipe the frosting onto the cupcakes and top with fresh pomegranate seeds.