It sounds like you are the heir of the deceased homeowner and/or the executor of their estate. As such it is now your responsibility to manage the assets and liabilities of the estate until probate is completed or the estate is otherwise settled. That includes paying the mortgage and, if appropriate, renting the property. You do not need permission from the lender to do that.

You do need to contact the lender and let them know that the homeowner has passed away. They will tell you what documentation they need to change the name and mailing address for the statements to the person responsible for the estate and after the estate is settled into the new owner's name. There is no requirement to payoff or refinance the mortgage loan.