Does paying off a car, and getting the Loss Payee removed from the car insurance, lower the car insurance rate for that car???
PRM may say otherwise, but I'm going to say no, your rates will not go down. That is not unless you drop some of the coverage or raise your deductibles that you had on the vehicle to satisfy the requirements of the financial institution.
Shop around. While dropping your lien-holder won't lower your rates, shopping around might. We had USAA, which was supposed to be the lowest around. But the rates kept going up, and we just switched and saved more than $250 a year. And that was with increasing one car from just liability to adding comprehensive. No changes to deductible (although raising that lowers your rates a lot) or other coverage. Also, check the coverage you have now. Don't pay for things you don't need. They often add in extras like medical payment coverage, which is not required in NC and only kicks in after your regular health insurance, so is virtually worthless if you have health insurance; or rental car reimbursement; or roadside assistance.
Med pay only kicks in AFTER your current/any other medical insurance. So if you're uninsured it might be worth the money, but if you currently have health insurance it may be a coverage that you just don't need. At least, that's what USAA and Farm Bureau both said their medical payment coverage works.