Most consumers are not aware that they may be able to lease a used car. By far, the most common way to purchase a pre-owned vehicle is to financing through with a traditional car loan.
Often, leasing a used car will not make financial sense. However, in certain cases it could be a viable solution.
First let me refresh you with the basics concept of an automotive lease. A lease is an agreement between the Lessee (customer) and the Lessor (leasing company). The Lessor sets a value for the vehicle at the end of the lease. This value is called the residual.
For example, after three years from the purchase date the leasing company might set the residual value of a $30,000 car at $15,000. Today, most leases are "closed-end" leases. This means the Lessor (leasing company) will own that vehicle for $15,000 at the end of the lease or the customer could purchase the car for that amount.
When leasing a new car the lessor can easily forecast the value of the residual. This is because they know the condition of the vehicles is brand new and it will depreciate at certain rate every year. Therefore it will be worth certain amount at the end of the lease.
However with a used car, they don't have a fixed "starting value" for the vehicle. Once a car is "used" it has a unique value based on miles and condition. So the Lessor must estimate the residual based on comparable vehicle's values.
The residual value is the primary reason that leasing a used car may not be a good decision. The Lessor is going to be very cautious when estimating the lease-end value. In other words, they are going to "guess low" and when a lease is structure with a "low" residual value the monthly payments are going to be higher.
Furthermore, the best leases on new cars are normally supported by factory programs. This means the factory will increase the residual value or lower the money-factor in an effort to sell more of their product. As a matter of fact, a used car lease payment is normally not much less that a normal car loan payment.
All that being said, there are a few instances a used car lease might make sense. For instance, some niche vehicles such as Ferrari's tend to have a stable resale value and Ferrari will provide pre-owned leasing programs. Also, many customers can realize certain tax advantages when they lease a vehicle.
You can read about leasing including money-factors and residuals here.