This is just a general question, based on some discussions I have been having: Can a landlord specify that certain items are not allowed in the apartment as part of the lease? I know that I've had leases that prohibited things like fish tanks, water furniture, and pets, which seems to say that they can choose to outlaw items if they wish. But could they put in a "no guns" clause? Or would the Second Amendment trump that? What about something like skateboards, which are not covered in any constitutional amendment?

Yes, the landlord can regulate that. The 2nd Amendment says that the government may not make laws that abridge those rights. It doesn't mean that a private party can't make those kinds of rules.

Yes they can, but they can't change it in mid lease. You will see stores, at least where I live that often have signs that prohibit guns.