Yes. Generally speaking, it would be lawful for the landlord to evict a tenant under such circumstances.
Frank W. Chen has been licensed to practice law in California since 1988. The information presented here is general in nature and is not intended, nor should be construed, as legal advice for a particular case. This Avvo.com posting does not create any attorney-client relationship with the author. For specific advice about your particular situation, please consult with your own attorney.
Since the landlord apparently did not put a "no pets provision" in the lease (or if the landlord did it was waived by accepting rent for two years knowing of your dog), the landlord may not be able to evict you by proving the pet problem was so severe as to amount to a "nuisance" or "waste" upon the premises under CCP 1161(4); Freeze v. Brinson, 3 Cal.App.4th Supp. 1, 5 (1991).
Why in the world would you want to stay? Do yourself a favor and move out.
If we do not have a signed fee agreement I am not your attorney and this is not legal advice.