For a proper answer, you really need to have an attorney read the lease. Not being responsible for the rental grounds is different from not being responsible for a tree that they know is a hazard.
There are plenty of good attorneys in the Cincinnati area. Search Avvo for a landlord tenant attorney. If you can't find anyone there, try the Cincinnati Bar Association Lawyer Referral Service, I have provided a link below, or the University of Cincinnati Law School Clinical Program. I have read what they post on their web page and nothing seems to fit exactly, but there might be some help there if you contact them. The clinical programs are free and have upper level law students represent you under the supervision of a professor.