Trim and cook artichoke bottoms. Bone lamb chops and sprinkle with salt and pepper. In large heavy skillet, sear chops in oil over moderately high heat for 1 minute on each side or until golden.
Melt butter and set aside to cool. Brush 1 sheet phyllo with butter, top with another sheet of phyllo and brush again with butter. Put 1 chop in center of phyllo, top with 1/4 inch slice lemon, peeled, 1 sprig dill and 1 artichoke bottom cut into 1/4 inch slices.
Sprinkle lamb with 1/4 teaspoon lemon juice, salt and pepper to taste, top with 1 sprig dill and 1 teaspoon grated cheese.
Bring together the 2 short ends of phyllo. Fold under lamb to seal package. Continue with remaining lamb. Put in buttered baking pan. Bake at 350 degrees for 20 to 30 minutes.
