Can a mortgage lender come after the executor if the estate has no money to pay?

I am so sorry for your loss and for the situation. The executor is generally not held personally liable for the debts of the estate BUT has the obligation to administer the estate fairly and make sure debts are paid. It sounds here like you are doing this on your own. That may not be such a good idea. It also sounds as if you have to make some hard choices on behalf of the estate, like either selling the property to pay the mortgage off or filing for bankruptcy - estates can be insolvent. Mishandling can get you in to trouble. Good luck.