Generally, the best time to lease a car is shortly after the model is introduced. That's when the residual value will be the highest - meaning you'll likely save money on the depreciation cost.
The residual values are usually based off the Automotive Lease Guide's Residual Percentage Guide which is updated every two months. As the model year progresses, the residual values trend lower.
If you were to lease a car for 36 months towards the end of its model year, the car would be considered a four year old vehicle when you turn it in. That means you're going to be paying an extra year's worth of depreciation.
The flip-side of course is that the negotiated price of a vehicle tends to head lower as the model year progresses, so there are pros and cons to leasing early. As long as you negotiate aggressively you should be able to negotiate a decent purchase price for your lease.
Be careful if the vehicle is a very hot seller. When the model is first introduced, the demand can be so high you may not be able to negotiate the price below the MSRP. If this is the case, wait two or three months for the supply to catch up to demand.
Assuming the car is not a newly redesigned model, one more reason to lease early is because most manufacturers raise the invoice and MSRP prices of their vehicles during the model year. Some domestic manufacturers raise their prices several times, which can add a few hundred dollars to the price of the vehicle (and thus raising your capitalized cost).
Most new models are introduced between July and October, so this is the time that you should try to lease to maximize your savings.
The only time it doesn't matter when you lease is if the manufacturer is offering special lease deals. These subsidized deals can include artificially inflated residual values, low money factors, or lowered capitalized costs which you should take advantage of whenever they are available.