Inherited tenant refuses to sign addendum. What are my options?

[Lettie T.]

I purchased a rental over the summer that was already occupied. The lease and other documents provided by the former PM clearly stated that there were no dogs in the household and that pets would only be allowed after a pet addendum was signed. As soon as I discovered the dog, I asked the renter to sign the pet addendum and started charging monthly pet rent.  I explained to him that until the addendum is signed, he is in violation of his lease. He is paying the pet rent but refuses to sign the addendum. What does this mean for me? Can I still enforce the addendum?

He told me that his dog had been living with him all along, and he did put on his rental application that he had a pet. However, documentation from the previous PM states that he said on more than one occasion that the dog was his ex-wife's, she got custody of the dog, and that the dog would never be at his house. So, he lied either to me or to the previous PM.

He also told me he paid a $250 pet deposit when he moved in. The previous PM doesn't charge pet deposits at all and the documents they gave me prove he never paid a pet deposit. So, he's lying to me about that as well.

His lease ends mid-January, so starting the eviction process now just doesn't seem worth it. Non-renewing would be much easier and less expensive. This is my first inherited tenant, so I'm not sure what to do in this case. Advice and suggestions are appreciated. TIA!