In a medium bowl combine the cream cheese, onion, parsley, dill, garlic and lemon pepper. Add crabmeat and mix thoroughly. Season with salt and pepper to taste. Cover and chill in refrigerator (can be prepared 2 hours ahead).
Using a small sharp knife, cut in half horizontally through the center of each chicken breast half, creating a pocket. Fill each pocket with 1/4 of the crab stuffing. Then dip each chicken piece into flour, eggs and finally bread crumbs to coat. Cover completely.
In a large skillet melt butter or margarine with oil over medium heat. Add filled, breaded chicken breast halves to skillet and saute until golden brown and cooked through (juices run clear), about 10 minutes each side. Remove from skillet, drain on paper towels and serve.