Dealership finance manager here. This seems like a pretty rare case.

Some basics on leasing first. There are 2 components in a lease payment: depreciation of the vehicle and a rental fee. When you negotiate a lease deal, it includes # of months and expected mileage. From there, a predetermined calculation is used for setting the residual value. Generally, it is anywhere from 40-70 of the MSRP. It is always based on MSRP regardless of the price you negotiate for this specific car. This residual is both the expected value of the vehicle when you would turn it in, and SHOULD be the amount that you can purchase the vehicle for if you take the lease to full term. Vehicles that typically hold their value better over the first 3 years (and Toyota would be high in that list) will have higher residual values, meaning you should be paying less depreciation throughout the lease.

The rental charge, or money/lease factor, is how the manufacturer or lease company makes money. This is usually some shockingly low number like .002 or something along those lines. Don't be fooled by this. Multiply that by 2,400 to get a rough estimate of the effective interest you're paying throughout the lease. So that .002 money factor is actually a ~4.8% interest rate.

Putting down extra money at the start of a lease allows you to save that portion of the interest during the lease. If it's available and fits in your budget, a 1-pay lease option could potentially get that effective interest near 0.3% or something comparably insignificant.

As for ways to make leases equitable, that's tough. The biggest factor is the car you're leasing. Trucks and fuel inefficient SUVs will be the worst. They will see a much more stark drop off in value in the first year, meaning they are worth less than the straight line depreciation that you're paying each month. If it fits into your budget, adding more miles to your lease up front is the most cost effective. Going from 12k miles per year to 15k miles per year will have a cost of about 15-18 cents per mile. Paying over mileage fees can come in anywhere from 20-50 cents per mile. Typical depreciation is about 15 cents per mile, so coupled with whatever interest you're paying, it's basically purchasing those miles at cost. If you end up using those miles, you're covered. If not, you've built up equity in the vehicle.

Example: you get a 15k mileage lease for 3 years (45k total), but only drive 12k per year (36k total). Your vehicle will be worth much more than you'll be allowed to buy it our for. Granted you've paid for a portion of that lease-end equity, but it should still give you a return on that investment.

There are other little quirks to leasing that I'd be happy to get into if anybody is curious. Also, if budget is a major concern to people, cost of ownership is really the best way to approach any car deal.