What are my legal options for a business that refuses to stop billing me for service provided as a lessee after I have moved out?

Upon moving out you should no longer be on the bill.  the owner of the house kept you on the bill so that he would not be liable for the services.  It appears that you are being taking advantage here and should not be on the hook so to speak for the bills that continue to accrue as you are not obtaining a benefit here.  If suggest ignoring the bills and in the event that you are sued, you want to seek indemnification against the owner of th ehouse as he is the person that must pay this bill.  I also suggest that you have a lawyer represent you if you are sued to make sure you are protected.

If you were both on the bill, usually what happens is liability is considered joint and several.  This means you each owe the whole but can seek contribution from the other for his or her share.

So in this situation by placing your name on the bill, you became equally liable but you should be able to take your name off and inform the company that you no longer live there.  Did the contract have an end date that somehow matched your lease agreement? Check the contract.

Further, you may wish to send a certified letter to your former landlord.  If he or she ignores it, you have proof to take him or her to court (most likely small claims) to get this matter resolved.