Like a loan, the monthly lease payment is reliant on the term of the lease, the implied interest rate and the initial "purchase price" of the car. The "lease-end" or "residual" value varies from a loan, but is still important. This is the value that is expected at the end of the lease term.
You are paying the difference between the initial purchase price and the residual value in a lease. The lowest purchase price should be negotiated, which will lower the cost of leasing. If you don't intend to buy the car at the end of the lease term and it is closed-end, you might want to negotiate a higher residual value. Make sure that your expected mileage during the lease aligns with the allowed mileage in the agreement. If it doesn't, you may pay significant penalties when you turn the vehicle back in to the dealer.