Cook pasta according to package directions, omitting salt and fat; drain.
While pasta cooks, bring wine, stock, and thyme sprig to a boil in a large skillet. Add lobster. Cover, reduce heat, and simmer 5 minutes or until done. Remove the lobster from pan, and cool slightly. Remove meat from lobster tails; coarsely chop.
Add oil, salt, and pepper to wine mixture in pan; bring to a boil. Cook 14 minutes or until reduced to 1/2 cup. Discard thyme sprig. Stir in cream. Add lobster meat and pasta to sauce. Cook 1 minute or until sauce coats pasta, and toss. Sprinkle with parsley and thyme. Serve immediately.