Place Maine Lobsters or Maine Lobster tails in boiling, salted water to cover. Bring to boiling; reduce heat and simmer 13-15 minutes, until done. Pour water off and cool. Remove all meat and cut into small pieces.
In saucepan, cook green pepper in butter until tender. Blend in flour; add milk. Cook and stir until thickened and bubbly. Add water chestnuts, sherry, paprika, and salt.
Cook and stir two minutes more. Remove from heat. Stir in Maine Lobster. Place in casserole server and sprinkle with grated Parmesan cheese.
Bake in 375 degree oven for 15 minutes. Serve warm as a dip, with toasted bagel chips.