Preheat the oven and prepare the baking pan.

In a bowl, combine flour, sugar, baking powder, baking soda, and salt.

In another bowl, cream together the softened butter and sugar until fluffy.

Add the eggs and vanilla extract to the butter mixture and mix well.

Gradually add the dry ingredients to the wet ingredients, alternating with buttermilk, mixing until just combined.

Fold in lemon zest and lightly mashed raspberries.

Pour the batter into the prepared baking pan and smooth the top.

Bake in the preheated oven for 30 minutes or until a toothpick comes out clean.

While the cake is baking, prepare the frosting by beating cream cheese and softened butter until smooth.

Gradually add powdered sugar, then mix in vanilla extract and lemon juice until well combined.

Allow the cake to cool completely before frosting with the cream cheese frosting.