It doesn't work that way, a lease is just a form of financing where the Future Value is higher than 0. Think of it as a balloon payment at the end. Take out the car and just think of it as an account with $$ in it.
Your capitalized cost is identical buy vs lease. You will pay a bit more interest on a lease because you are not paying down the principle as fast (3 yr lease vs 3 yr note) but a 0.9% (what I see on a lot of leases as the money factor as well) it's negligible, and IMO a worthwhile cost for the downside protection on the value. Even at 2.9%, it really is not that much of a difference.
Even for higher resale vehicles, you either benefit from the much lower lease payment over purchase, or you end up with value over the residual, which is only sunk if you turn the car in. Buy it at the end, roll into another 60 mo loan at 2.9% and keep stretching the payment out. I'll let the bank own my car at 3% and use the money on other more profitable endeavors. Yes, that would mean financing for 8 years, but you are only paying for what you are using, it's an expense (I don't recommend this unless you have full control of your finances... this is not a way to afford a car you otherwise couldn't, use the savings to grow your money in other areas).
I have crunched the numbers 6 ways from Sunday, and it really doesn't matter IF you are buying new. Disclosure... I own my 4R, leasing a VW Jetta. Reason? I don't trust the Jetta to be worth what the residual the dealer gave me, and won't keep it because I don't trust it to not give me trouble past the warranty. The cost to own I believe to be lower to lease in this case, plus you don't get as good of an interest rate when you finance less than 15k.
A little back on topic, to the OP, Leasing a Civic isn't the cheapest way out, but if it is what you want and can afford it, go for it and negotiate it just like you were purchasing the car (push for cost, even though the dealer is going to be talking in monthly payment terms, understand how it's calculated and get where you want to be). Just admit to yourself that you want it, and that is why you are going new Civic vs a 10 yr old used vehicle. The financials between those two do not work out in favor of the lease.