Melt butter in a large pot over medium heat. Add onion; cook and stir until tender, about 10 minutes. Add flour; stir until combined and cooked, 1 to 2 minutes. Pour in milk; cook and stir until thickened, about 5 minutes. Add heavy cream and lobster, stirring constantly, until bisque re-thickens, about 5 minutes.
Stir cooking sherry, paprika, and Cajun seasoning into bisque. Cook until flavors combine, 2 to 4 minutes. Season with salt and black pepper.