In other news, I've toyed with the idea of electrifying a Lotus. Obviously that is called a Tesla roadster and I doubt we could do it as well, but it would be a cool project.
I've thought about this idea as well. On the one hand, you'd be a parts integrator without access to OEM design resources. On the other hand, there are a lot more EVs on the road than there were when the Tesla roadster was designed and the pool of parts, technology and methods is a lot deeper. Also battery (and battery management) technology continues to advance, which is how the Tesla Model S keeps increasing in performance with the same platform, envelope, and drivetrain.
I suspect you could put the battery capacity of the roadster in a 20% smaller package than it used. The 18650 cells generally used for traction batteries are easily packaged in all sorts of odd shapes, and it happens that there are a lot of interesting voids in the Elige that you could stuff batteries into - the door sills for instance. This could have the effect of improving the polar moment of inertia over even a stock Elise if the motor/transmission/electronics package is lighter and more compact than a 2ZZGE + six speed. The fuel tank void behind the seats is also a convenient shape that would efficiently swallow a good sized battery all by itself.
Further, if you cooled the motor and electronics with the oil cooler ducts, almost all the water plumbing and radiator weight (and heat) goes away, and a lot of volume around the footbox becomes available as well. Ditching the radiator makes it easier to air condition should you still feel the need.
Frankly, it's a lot easier to usefully electrify an Elise than many other platforms I've seen - it's not wedded to an IC engine driveline shape, and there are several good places for the batteries and electronics. It would be a lot harder to electrify a Corvette well, for instance.