My guess is that it will be based on the new VVA chassis (Versatile Vehicle Architecture http://www.gglotus.org/ggrace/vva-chassis/vva-chassis.htm). It will grow in size (probably longer wheel base), though not considerably, with a tad more creature comfort. It will therefore become heavier, with a bigger engine it will need a stronger subframe = more weight, although I think Lotus will try their best to keep it below 950 kg. Comparing this weight with the competition it is still low. The chassis will get stiffer, to balance out the gain in weight. It will be rawer and more spartan to drive than the Evora. It will get less power than the Evora.
Regarding the design, I think it will get rid of all the plastic grills/fins, as they look a bit outdated, the rear lights will be single lights on each side, like the Evora, the new 458 Italia, etc...these are all new car design trends.
I have no idea about what engine they might come up with. But I wouldn't be surprised if Lotus came up with a very green engine.
Personally I would like Lotus to take the Elise back to its roots, e.g. make it lighter (approx 800 kg) instead of increasing the power and creature comforts. But this is more difficult than it sounds, going back to 800 kg with today's standards (also security constraints) will make the development and hence the sale price expensive.
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