An Insurance Lawyer deals with all kinds of problems related to Insurances. They are often able to make deals with the insurance to avoid a court case, but if they aren´t they are more then able to take on an insurance in court.
For example your insurance company claims you have frauded it in a car accident or you have been involved in a car accident and they don´t want to pay, these are typical cases for such a lawyer.
A more unique case would be Asbestos in your home, which has led to Mesothelioma (a form of cancer).
In such a case your best bet would be more specialized lawyers like an Asbestos Attorney and/or a Mesothelioma Lawyer. (Side note: Asbestos was used in many homes build between the 1960s to the 1990s. It was used all over the US, but most often in Arizona and Florida)