That's a bit complicated and, first, depends on the exact terms and conditions of the contract.

Sometimes a contract will specify that the contract is the only agreement and that anything agreed outside the contract doesn't count.

Sometimes a contract will specify that failure to enforce a condition is not a waiver of the condition.

Sometimes a court will rule (under common law) that those two elements exist and sometimes not.

I suggest you take your contract and your situation to an attorney and review your options. If you don't want to do that, you'll just have to wait and see if the landlord does terminate your tenancy because of the dogs and handle it when it happens, either by moving or getting an attorney.

Bottom line, though, is that you signed the lease that said one dog when you knew you had 3. A judge could easily rule on just the words written in the contract and leave you with the consequences of doing that.