A court will most likely uphold such a lease restriction. Contract law applies - not constitutional law. You can bargain away any right you wish (absent, of course, violation of certain laws; e.g., you cannot bargain away your right to life and contract with someone to kill you - that would be conspiracy to commit murder). When you negotiate terms of a lease and agree to abide by its terms in exchange for possession of the property, you have established what courts call "consideration" which, roughly speaking, is a bargained-for benefit to the parties. Generally, when consideration is present in an agreement, a binding contract exists. Accordingly, the responsibilities, including firearm restrictions, bind the lessee while the benefits of that contract - possession of the property - inure to the lessee.
Constitutional law is not an issue here. The Constitution (at least the US Constitution - I do not speak to those of all 50 states), exists to limit the powers of the federal government, not to put checks on individuals rights of contract. For example, the first amendment gaurantees that Congress may not pass a law establishing a religion. It does not, however, restrict, for example, a home owners association from establishing a bylaw that everyone who is a member must be a practicing Jew or Christian or Muslim. The Constitution does not restrict private actions at all - only those of the federal government.*
The cases you cited deal with the powers of government to restrict individual liberties. While we may wish and think of possession of a firearm to be a "fundamental right," the Constitution neither protects such rights against another private individual nor retricts your right to bargain them away.
* To be complete, the Constitution does restrict state governments as well - e.g., preemption of state law through the supremecy clause, the commerce clause, and the contracts clause. It does not, however, restrict individuals.