Could he evict me or sue me for getting a dog after he already said a no-pet policy even though it is not mentioned in the lease?

You should have left well-enough alone. If your lease was silent on the pet issue, you probably could have gotten away with getting a pet. However, since you formally asked for permission (in writing) and permission was formally denied (in writing), there is now a potential dispute. A court might not be sympathetic since you now know it would be against policy. I would suggest moving elsewhere after the lease is up, if you want a dog. Good luck.

Your question requires an attorney consultation. It is not a simple question that can be answered on this type of forum. There are many factors that would need to be considered and evaluated. I strongly suggest that you contact an experienced landlord/tenant attorney for a face-to-face consultation and give him/her all of the facts surrounding your situation. He/she would then be in a better position to analyze your case and advise you of your options.

Your Landlord can try to sue you for breach of the lease agreement subject to your defense that within the terms of the lease there is no explicit prohibition of pets. The Landlord has the burden to overcome that defense and show that even without the express language you knew or had constructive notice of his no pet policy. Your Landlord can try to evict you subject to your defense(s). In both claims it appears that your landlord's claims will fail, albeit I do not know all of the facts, however on what is known, you can successfully defeat either claim.

He could not evict you unless he had specific evidence that your possession of a dog violated some other lease clause. The reason that landlords put no pet clauses into their leases is that without them you have every right to have a pet, so long that it does not damage the premises or interfere with the quiet enjoyment of other tenants.

See and attorney, it may be that you will be able to stay out the lease, but I doubt it will be renewed if you insist on keeping the dog. The answer is in the writing.