Preheat an oven to 350 degrees F (175 degrees C). Grease and flour 2 9x5 inch loaf pans.
Mix flour, baking soda, baking powder, and salt in a bowl. Set aside. Beat the butter and sugar with an electric mixer in a large bowl until light and fluffy. The mixture should be noticeably lighter in color. Add the room-temperature eggs one at a time, allowing each egg to blend into the butter mixture before adding the next. Beat in the avocado and lemon juice with the last egg. Pour in the flour mixture alternately with the milk, mixing until just incorporated. Fold in the lavender and lemon zest; mixing just enough to evenly combine. Pour the batter into prepared pans.
Bake in the preheated oven until a toothpick inserted into the center comes out clean, about 1 hour. Cool in the pans for 10 minutes before removing to cool completely on a wire rack.
