I would go the route of saying you're "thinking of getting a small caged reptile" such as "maybe a turtle or a gecko or something" and then if pressed say that the opposite person to the one who is on the phone is the one thinking of getting it. They probably won't ask more specific questions after that and in that case, as long as they have not specifically returned with "well, as long as it's not a snake" and your lease does not say no snakes, you should be fine. The semantics of it are, of course, incredibly important. You have to say "or something" to assume their answer includes more than turtles or geckos.

It might also be the snake type. Our leasing agent was fine with us buying a corn snake but very leary of a ball python. They eventually returned with "you can have a small snake." I figure our currently 150g girl is pretty darn small.