As long as you continue to live there, you need to pay rent. Your landlord's obligation to pay the mortgage has nothing to do with your obligation to pay your rent.
Attorney Inga Stevens is licensed in Maine. She provides general information on Avvo.com. No attorney-client relationship arises out of the information given here.
In general, you should continue to pay the rent even though the house is in foreclosure. I have made the argument that the landlord is committing fraud by accepting rent and not paying the mortgage but the judges have universally said in essence, that "they don't care", you still have the obligation to pay the rent or face eviction.
The problem you have is that it is a lease option or rent to own situation. Any portion that you paid as a deposit or as part of your rent that would go towards the purchase price might be lost if the landlord is falling behind on the mortgage and in financial trouble. Perhaps you could negotiate something with your landlord, such as reduced rent. Sometimes there are also provisions in mortgage documents that if the landlord is in a state of default on the mortgage, that the tenant should pay the rent to the bank rather than the landlord.
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I have to disagree with the other attorneys. Depending on the terms of your rent to own agreement, you may be able to stop paying and avoid eviction but it is not something that you can do on your own. You need an experienced real estate attorney to advise you. Technically a rent to own agreement is not governed by the residential landlord tenant act so you should be able to stop an eviction but it depends on the attorneys knowledge and how quickly they act.
I provide a free 15 minute telephone consult for security deposit claims and eviction defense. No attorney-client relationship is created by answering questions in this public forum. If you wish to create an attorney-client relationship, you must contact me directly and sign a representation agreement. Answers are provided based on general ideas and an answer specific to your situation would require a review of all documents.