Legal Question in Landlord & Tenant Law in Illinois

You may be looking in the wrong place in the lease. I am sure it says the tenant can not cause damage to the common areas (and usually a courtyard is a common area), and allowing a pet to relieve itself in that common area can cause damage (browning of grass), or at least it could be a "nuisance" which most leases also do not allow. So there may not be a specific rule, but enough in the lease, to cover the issue. Other than that, you are responsible for controlling your pet, so it is not unreasonable for management to insist that you get your pet beyond the property or that you be responsible for any damage caused. If the only way out of the property was a hallway in the building, I'm sure you'd agree that it would not be o.k. for the pet to urinate in the hall.