"Based on our understanding of the facts, the library is not a party to the No Trespass Order, so they should have no duty to ensure that the order is enforced. Indeed, it is probably best for the library not to be involved in the dispute between the landlord and [third party]. Unless or until (1) the [third party] cause issues with the library directly, or (2) the landlord formally involves the library, the library should continue to conduct its business as usual."
A library board may submit such requests as long as no library resources were used; i.e. no library computers to send the message, and no official letterhead. Advocacy should be done from personal computers on personal time.