Melt the butter in a medium saucepan over medium heat. Slowly cook and stir mushrooms in the butter until tender. Mix in lobster meat. Cook until opaque. Remove mushrooms and lobster from saucepan and set aside.
Reduce heat to low. Place flour in pan. Cook and stir approximately 2 minutes, then stir in chicken broth, heavy cream and pepper. Simmer 5 to 10 minutes, or until thickened.
Stir mushrooms, lobster and Parmesan cheese into the sauce mixture. Continue cooking 5 minutes.