If the lease is month to month, that means that the landlord can give you a full month's notice, and terminate the lease. Setting the pet aside, the landlord can have you out of the property in about a month. So, given that, if you have a pet and want to stay, you will have to abide by his terms.
That said, if the pet is somehow related to a disability, you may be able to change that result.
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Ask why the change to your lease - first. Get the whole story from him. Maybe he does not have a real reason to increase it. But if he does, you may want to reconsider going through the legal motions on this one. Has there been any pet damage in the past? Are you housing more than one animal OR more than the lease allows?
As for the month to month tenancy in NC - he is going to have to give you a full period's notice. That means that if he decides to change and notifys you in the middle of your term/period, he will have to wait until the end of that term and one more term to make any chages to your lease. There must be at minimum a full term's notice. Even though you have been there five years, you are now on a month to month tenancy. This can change for you or against you. Its better to work with what you have and try to work this out. Best of Luck!