Yeah I was going to say. Earlier estimates of 10k seems very low.
You'd have an easier time doing something more like a Nissan figaro.
It has a cloth drop-top but the frame of the car remains in place. For the emira it would be smaller, and likely fully removed instead, but this idea.
The Emira has frameless doors, so without the roof section the windows will lose vital parts they need to seal against, not to mention the rear 3/4 glass would have to go somewhere if you pick the roof off.
Overall, there are a lot of cars offered in a sports trim that have factory convertibles. While a number of Lotus vehicles have come convertible, I feel like they always design the car ground-up for that purpose. For the same money why not find a slightly older Aston? A DB9 Volante would cost 1/2 what the Emira does.
Otherwise if you are after the handling and so forth, you could look at Boxster GTS or Boxster Speedster