If you know you're going to give the car up in 3 years - lease.
If you know you're going to keep it - buy it.
As others have mentioned, it depends on the terms. But if you know you're going to sell the car, then not only are you paying interest on the money you've borrowed to buy the Elise, you also will eat the depreciation on the car when it comes time to sell. If you're the gambling type, you could hope that Elise-mania holds up for three years, and then you would not be hit hard by this. But I don't think the Elise will be extraordinary in this department, not 3 years from now.
If you are going to put lots of miles on it (daily driver/lots of commuting/road trips) - leases usually have high mileage penalties.
Track days - if even track days are forbidden (as opposed to competitive events) - I guess the risk in ignoring this prohibition is, what if you crack it up on the track? If you make a claim on insurance, they'll know. If you don't, the repair cost might outweigh the money you saved.
If you like to mod the cars - you have to choose reversible mods (ones you can economically roll back - if you bored and stroked the motor, it would probably be pretty expensive to revert back to stock.
If there is no prohibition on track days (or you're not worried about a traceable mishap), and the residual is anything close to reasonable, lease.
If there is a prohibition, buy. If you can't use the car for the purpose you intend, what's the point?
I'm guessing, unless the Elise turns into the next Pinto, with some grievous safety defect, the Elise's resale value will hold up fairly well. It might be close to a wash if you get a good interest rate.
Though of course, in the end, just do the math as others have advised based on your options...