Place salmon in a shallow dish, and rub with 3 tablespoons lemon juice. Season with dill weed and lemon pepper. Cover, and allow to stand 10 to 15 minutes. Heat 2 tablespoons butter in a saucepan over medium heat, and sauté shallot 2 minutes, until tender. Mix in remaining lemon juice, vinegar and 1/4 cup chicken broth. Simmer until reduced by at least 1/2. Stir in cream and milk. Season with dill, parsley, thyme, salt and white pepper. Cook and stir until thickened. Whisk in 1/4 cup butter. Set aside and keep warm. Heat remaining 1/4 cup butter in a skillet over medium heat. Place salmon in the skillet, skin side up, and cook 1 to 2 minutes, until seared. Set salmon aside. Deglaze the skillet with remaining 1 tablespoon chicken broth, then mix in the cream sauce. Return salmon to the skillet, and cook 8 minutes in the sauce, or until easily flaked with a fork. Serve with the sauce.