If you sign a lease for a year giving you permission to have a dog can your landlord break this lease ? There have not been any problems involving the dog.

As far as I know, no.
But what is happening is that many insurers are canceling policies of homeowners and landlords when dogs are present, or certain breeds or sizes of dogs are.
That is not your fault, of course...
What has your LL used for a reason?

No, if the lease specifically sated you were allowed a dog, then the landlord can't break your lease over that. He could inform you that he was not renewing your lease.

Lets clarify, you have a lease which allows a dog and the LL broke the lease. However, we do not know why it was broken, there is a loose assumption it was due to the dog but you must be more specific. Please answer joy's question, what reason was given?

And what OP means by "break lease" needs to be specified.

If the LL simply told OP "your lease is ended", OP's response should be "no, it isn't."

The bottom line is this: from what we have been told, the lease is still in effect. Anything LL actually does contrary to that position would be incorrect.