In a small bowl, combine the anchovies with the lemon zest, lemon juice and 2 tablespoons of the olive oil. Season with salt and pepper.
In a large skillet, heat 1 tablespoon of the olive oil. Add the zucchini, season with salt and cook over high heat until browned in spots; transfer to a large plate. Add 1 tablespoon of the olive oil and the mushrooms to the skillet; season with salt and pepper, cover and cook over moderate heat until starting to brown. Uncover and cook until tender and browned; transfer to the plate.
Season the scallops with salt and pepper. Heat the remaining 1 tablespoon of olive oil in the skillet until shimmering. Add the scallops and cook over moderately high heat until browned on the bottom. Turn the scallops and cook for 1 minute longer; transfer to a small plate. Add the shallot to the pan and cook until softened. Add the wine and simmer, then stir in the zucchini and mushrooms and reheat. Swirl in the anchovy dressing, any scallop juices and the butter.
Arrange the lettuce on plates and top with the scallops and vegetables. Garnish with the chives, tarragon and bottarga and serve.