You are not required to put cash down (capital cost reduction) on a lease. Usually the only requirement is first monthly payment, security deposit, and, in some states, taxes. The first payment and security deposit are sometimes waived (or paid by the manufacturer as part of a special promotion) and, in states that do not require taxes upfront, the dealers are able to advertise $0 due at signing. However, whenever you see a lease deal advertised at a really low payment, the dealer is usually just trying to advertise a "price leader" and they will include a capital cost reduction in order to lower the payment. You are only required to put the cash down if you want to drive out at that payment. Another thing with low advertised lease payments is that they usually advertise the base models (few options). So, if you want things like leather seats, power windows, cruise control, sun roof, etc., you will have a higher payment.

My two cents.