You may very well have legal grounds against the tenant and your landlord if he isn't willing to stand up for you. It would be one thing to have you being the one moving in with your neighbor already living there. But, with you being there first, you should have some rights.
A concrete case could be made that your landlord didn't have an issue until Broom Hilda moved in and started trouble. I would stand my ground and let both your neighbor and your landlord know that YOU have rights as well. On the flipside of the lease not mentioning reptiles, it also doesn't say you CAN'T have reptiles. That plays into your favor, along with the fact you've been living there up to this point and your landlord knew you had these pets.
Stand you ground and tell your neighbor to get bent!