Even with a reverse mortgage, there is a lender - they are just "lending" out the money over a period of time (the monthly payment you receive), rather than all at once (i.e. so you could buy the home)
Did you get a Form 1098-INT from the institution that is servicing the mortgage? In any case, whoever is issuing your monthly checks is probably the lender. You should check with the broker or financial advisor that put the reverse mortgage together.