Melt butter in 3-quart saucepan over low heat. Cook onion in butter, stirring occasionally, until tender. Stir in flour, parsley, salt and pepper. Cook, stirring constantly, until mixture is bubbly; remove from heat.
Stir in milk and broth. Heat to boiling, stirring constantly. Boil and stir 1 minute. Stir in lobster. Heat to boiling; reduce heat. Simmer about 3 minutes, stirring frequently, until lobster is white.