+1 Spats. In addition, most states have statutes saying that a person cannot legally carry a gun on private property if he or she has been notified in writing that possession of firearms is prohibited there. This is different than specifically-worded signage that may be required to prohibit legal CCW by a CHL holder in a business that's open to the general public; I'm talking about other forms of written notice on property that's not necessarily public, such as an apartment.
IMHO a lease that prohibits firearms would certainly constitute proper written notice. If a lessee uses a firearm in self-defense, he or she may be vulnerable to charges of illegally carrying a weapon or even committing criminal trespass, even if the legality of the shooting itself is beyond question.
It is foolish to assume that "My Rights Will Protect Me" or "Legal Self-Defense is Always OK" in such circumstances.