Preheat the oven to 350°F (175°C). Grease and flour a baking pan.

In a mixing bowl, cream together the butter and sugar until light and fluffy.

Add the eggs one at a time, mixing well after each addition.

Stir in the vanilla extract, lemon juice, and lemon zest.

In another bowl, combine the flour, baking powder, and salt.

Gradually add the dry ingredients to the wet mixture, alternating with milk.

Fold in the shredded coconut.

Pour the batter into the prepared pan and bake for 30 minutes or until a toothpick comes out clean.

In a bowl, beat together the softened butter and powdered sugar until smooth.

Add the lemon juice and coconut cream, mixing until well combined.

Spread the frosting over the cooled cake.