Unless the seats are specifically made for the Elise then hardly any fit.
Or you can fit only one seat and keep the standard passenger seat, or remove the passenger seat completely.
The only one that has a chance of fitting is the Cobra Monza, but even with his one you can't really fit 2 at the same time unless you don't mind that the driver's seat can't be moved back very far anymore and it's interfering with the passenger seat. This is installed by KMS in Japan I think..
Lotus sells a Corbeau motorsport seat, but you can only fit one on the driver's side. They just re-cover the passenger seat in the same material/colors, because 2 of these would not fit in the car.
Biggest problem is often the width of the shoulder area and the width of the seat base, which causes problems with either the passenger seat or fitting it between the chassis side-beam and the center console.
A big problem is also to fit the seats low enough. Unlike most other cars the seats on the elise actually drop *below* the runners at their lowest point, so most side-mounts are way too high and you need custom brackets made. Otherwise you feel you are sitting too 'high up' (a common complaint with the Lotus/Corbeau seat)
This gets especially tricky if you want to keep the driver's seat slider as the seat bottom needs to be profiled to clear the adjustment mechanism and no off-the-shelf aftermarket seats have this AFAIK
For this reason there are several aftermarket seats available for the Elise (for instance Reverie carbon seat http://www.reverie.ltd.uk/shop/products.php?g1=b29f82
seats) , but not from the 'big' names like Sparco, Corbeau, etc.
Most of the aftermerket seats are meant to be bolted in place and use fixed seat mounts though.
Structural 'oddities' of the Elise also mean that you have to plan/design where/how to attach/anchor seat belts/harnesses.
For instance you can forget using the floor panel under the seats. It's totally non-structural and way too weak to attach any belts, even with load-spreader plates (not to mention that you'd have bolts sticking out under the car, ready to 'catch' on things).
You need to use the chassis beam(s) and seat mounts/rails for this purpose.
It's not rocket-science, just needs a little more planning and thought than in 'normal' cars.