Preheat your oven to 350°F (175°C). Grease and flour the 9x13-inch baking pan.

In a saucepan, combine the blackberries, dried lavender, water, and granulated sugar. Bring to a simmer over medium heat, and cook for about 5-7 minutes until the blackberries break down and the mixture thickens slightly. Remove from heat, stir in the lemon juice, and let it cool.

In a large mixing bowl, beat the softened butter and granulated sugar together until light and fluffy, using an electric mixer.

Add the eggs one at a time, mixing well after each addition. Then stir in the vanilla extract.

In another bowl, combine the flour, baking powder, and salt. Gradually add this dry mixture to the wet mixture, alternating with the milk. Begin and end with the dry ingredients. Mix until just combined.

Pour the cake batter into the prepared baking pan and smooth the surface.

Drop spoonfuls of the blackberry lavender mixture over the top of the batter. Using a rubber spatula or knife, gently swirl the mixtures together to create a marbled effect.

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

Allow the cake to cool in the pan for about 10 minutes before transferring to a serving platter.

Garnish the cooled cake with fresh blackberries and a sprinkle of powdered sugar for added decoration.