The Lamborghini Jalpa Spyder prototype.

created, based on a silver metallic over blue leather Jalpa which was still owned by factory, a similar rear treatment as found on the Athon was used for this special Jalpa, but the finished car didn't look as good as the Athon.
When looking at the Jalpa Spyder from the side, you would immediately see the problem, the rear was out of proportion compared to the rest of the car. The engine cover en tonneau cover were just too large for the Jalpa, the passenger cell was too much forward on this car.
The Jalpa Spyder actually had a working top designed for it, as you can see on these images, probably a good idea would have been to include a hard-top version too, but unfortunately it never came this far.
The Jalpa Spyder project was set aside, the management at that time didn't think they should actually offer the Jalpa Spyder in this configuration, it didn't look exotic enough to be a Lamborghini, although I personally think it would still sell, after all it was an open top Lamborghini, the only official 'new' convertible Lamborghini at that time.

Their have been 2 prototype chassis one was ready and drivable to other was just an unpainted chassis. They were later forgotten at the factory, they latest information of Stefano Pasini is, that the two cars have been sold to Tonino Lamborghini. The image shows the drivable car somewhere on the factory grounds in Sant'Agata. But it is somewhat hidden from view, it was in a very poor state at this time, rear flat tire, a dent in the door and the front spoiler now probably is mounted on another Jalpa.

Eric Thomassey found 2 Pictures showing the 2 Prototypes at the Factory in 1986:

We can see that one car is based on an early jalpa because the mirror is on the front wing, for the other car it is a 1986 body, I can see difference in the inside of the body that was common to the late Jalpa, different steering rack and different wiring that need different hole than on the early cars

In September 2001 during the presentation of the Diablo sucessor Murciélago, the drivable Jalpa Spyder was present in Toninos Museum at Dosso. It was restored in a very questionary way. The front spoiler looks like stolen from a Ferrari 348. I suppose they tried to restore the car with the remaining parts they found at the factory or bought a crashed Jalpa to take parts of it. There are no longer front spoilers existing as spare parts, therefore they made an own designed one, the look doesn't convince really, imo it would have been better to copy an original one.

On the rear end you can see that they used a American Exhaust designed for catalysts, the lights are again like Ferrari and sure not Lamborghini or Jalpa originals. The spare parts situation could be bad but with the original Urraco/Silhouette/Jarama Lights used in 1982 the car would make a better appearance for sure.

The Interior looks also very strange compared to the Prototype based on the silhouette chassis, but Lamborghini had allways a lack of money and parts. I'm sure the car Tonino bought from the factory had no interior at all, because it was used for other cars. On the windscreen surrounding you can see it's a very early chassis, the mechanism of the roof lock is identically to the Black Jalpa featured in the car magazines in 1982 with Chassis-Nr. CLA12002.

On this three quarter view the lines of the car don't look so bad. I think this car could have been restored much better to original Condition how it was in 1982. Perhaps it would have been better a Lamborghini or Jalpa Fan could be the Restorer of this unique car. I'm sure the car would look like a normal Jalpa all around except the cut off roof.

Overall I suspect this Jalpa is Chassis #1, it was built in 1982, has the same roof mechanism as Chassis #CLA12002 and was another Prototype at the side of the shown Prototype based on the Silhouette.

And in 2014 we were finally able to find the prove in the engine bay at Feruccio Lamborghini Musuem: