Okay, I can help you here.
First of all I would not lease the car for 60 months. In fact, I wouldn't lease the car for 48 months, but 48 months is the absolute max a car should be leased. Reason being when you get higher in mileage you start getting into more expensive maintenance items (tires, brakes, belts, etc) that you'll have to do to a car that isn't your property. 24 month leases are great but they're too expensive monthly, 36-39 months is the sweet spot. If you want to keep it 5 years I think you'd be better off buying, even if you can deduct the lease for business.
You absolutely can and must negotiate the price before the lease. In fact don't even tell them you're going to lease until you've agreed upon the purchase price in writing. The dealer will try and negotiate using the lease payment and they can hide profit easily that way. You want to look at the capitalized cost (the agreed upon purchase price), the money factor (multiply this by 2400 to get an approximate interest rate), and the residual. You want a high residual and a low money factor.
Now on to down payments. Resist the urge to put the trade in money from your '02 down on the lease for several reasons:
1. If you should total the car the insurance company will pay the owner, Lexus Financial (or whatever bank) and you would loose your downpayment.
2. A lower payment means a lower tax deduction for business.
You're better off putting the money in a money market account and write the payments or a portion of the payments out of that. If you must put it down, take advantage of the Lexus multiple security deposits instead.
Now as for december to remember. I actually disagree that December to Remember is the best time to lease or buy the car. They don't subsidize leases on the LS, so there won't be a special lease deal. They actually create artificial demand with all the marketing they do. In my experience you'll get a better deal in January when business is really slow.
Leasing is slightly more complicated though because residuals may be lower in January than they are now.
Check out this site:
www.leasecompare.com
Good luck! Keep us posted!