Preheat oven to 350 degrees F (175 degrees C). Grease a fluted tube pan (such as Bundt(R)) with cooking spray.
Combine cake mix, water, eggs, butter, instant pudding mix, and 1 tablespoon lavender in a large bowl. Beat with an electric mixer on medium-low speed, occasionally scraping down sides, until smooth, about 2 minutes. Pour into the prepared tube pan.
Bake in the preheated oven until a toothpick inserted into the center comes out clean, 40 to 50 minutes. Cool cake in the pan, 10 to 15 minutes. Invert onto a wire rack and allow to cool completely, about 30 minutes.
Mix lemon frosting and 2 tablespoons lavender together in a small bowl until combined. Spread over cooled cake.