While it is true that it does come down to what someone personally prefers, doing a large down payment on a leased vehicle extremely rarely makes sense since the risk of losing that capital is high. When leasing, paying more than the absolute minimum amount necessary is putting your money at risk with virtually no benefit.

A very small case can be made for times such as these when interest rates are low and investment opportunities are generating low returns, that the money saved by putting more money down can beat the amount that you would earn by spreading the payments over time and paying the additional interest on those payments. This is a risky endeavor because of the aforementioned risk of losing the car, and your down payment. True, GAP will pay off the rest of the lease payments, but you will still be stuck with the loss of a large wad of cash which you will have no recourse of getting it back. True, a car that gets totaled or declared a loss at the last few payments of a lease will have made yourself some money, but the risk is just too high. And any dealer that will sell you a lease without GAP is certainly a dealer to stay far away from.

If you want to spend some money, put down multiple security deposits. This is money that will earn you no interest, but will lower your payments at a decent clip, and will be refunded to you in the event of a complete loss.

To answer the OP, most car manufacturer web site lease calculators notoriously calculate high payments. This is done so that they don't undermine any dealers that may be applying a "stupid tax" to the lease.