If an insurer thinks that someone violated their obligations under the policy, or even committed fraud, they may investigate and/or refuse to pay. If you don't comply with their investigation or satisfy their concerns, they won't pay. But they can't do this arbitrarily; they have their own obligations under the policy and if  they don't honor them--e.g. don't pay when they should have paid--you can take legal action; that is, you can sue them, to force them to honor the policy and pay, if you think that they should. You should consult with an attorney with experience in forcing insurers to honor their obligations--there are attorneys who specialize in this--to evaluate your situation. Do that before doing anything about the lie detector test--either taking it or refusing it. Odds are the attorney will tell you to *not* take it, but get his/her advice first.