Preheat oven to 350°F. Butter or spray a cake pan that is at least two inches deep and line the bottom with parchment paper.
In a mixing bowl, whisk together the flour salt, sugar, baking soda, and baking powder. In another bowl, mix together the olive oil, 1 1/4 cups milk, eggs, lemon zest, lemon juice, and limoncello. Combine ingredients in one bowl and mix together until incorporated.
Pour batter into the pan and bake for one hour. Cake will be done when the top is a golden brown and a cake tester comes out clean. Allow pan to cool on a rack for 30 minutes.
Run a knife around the edges of the pan, flip pan onto cooling rack to remove cake, and allow cake to fully cool for two hours.
While cake is cooling combine powdered sugar, 1-2 teaspoons milk, vanilla extract, and ground culinary lavender in a mixing bowl. (Optional) Add several drops of red and blue food coloring to the icing for a desired lavender color.
After cake is cooled, add icing on top and spread around with knife allowing frosting to drip down the edges of the cake. Garnish with edible decorations and serve.