In a small frying pan place 1/4 cup chicken broth and the onion. Cook over a low heat for 5 to 7 minutes.
In a medium size pot over medium heat melt the butter. Slowly whisk in flour. Whisk until a creamy mixture is created.
Gradually pour in broth, whisking constantly. Whisk in milk, salt, onion, lobster meat, Worcestershire sauce and cayenne pepper. Heat until soup is almost boiling. Do not boil the soup as the milk will curdle when boiled.