As Corona only have cilindrical and spherical for now i made this to bypass that limitation.
As guide a typical spherical image are something like this:
This kind of images Corona can handle but in the other hand
A
hemispherical ligthprobe is something like this:
This sadly... Corona can render yet.
But don't be afraid... we can do it in no time!... a great
hemispherical ligthprobe image rendered in Corona (with some help).
JUST:
Render your scene using a CoronaCameraMod to obtain a 2:1 ratio image (twice the width as height) and save it in jpg, png (or hdri if you intend to correct it later).
Load that image as environment using VrayHdri map. Hide all your model and ligths and change renderer to Vray.
In Render Setup (F10)-> Vray-> Vray: Camera change camera type to Fish eye and check "autofit" dont forget to change your resolution to a Width=Height (1024x1024 by example) to obtain a fast 180° hemispherical panorama. (I think those are calle chromeballs).
This projections are used to ligth a sky domes or lighten a planetarium.
You can even take a step further and make an animation of it like some cool sky timelapses that hiperfocal design are showcasing.
As side note: if you render some hughe resolution, doing a full size render of the initial spherical panorama could can eat some RAM (and why to render some you dont need) a workaround for that would be using render región (available in VFB Settings, just change native Corona VFB to native 3DSMax and set a proper area of interest). This way you select the area of interest and render it and not the whole image.
Another posibility if your RAM is scarce coul be using the same aproach of Render region but this time render a lot of small parts of the image to compose later in some image stitchin sowtware.
Hope this helps.
Resume:
Render a spherical 2:1 pano in Corona with CoronaCameraMod
Load the result as VrayHDRI
Hide absolutely all and render with Vray fisheye camera type override (autofit).
And that's it... an awesome great fisheye render of your scene using Corona with a little help.
Note 1: A better way to do it is using the VrayDomeCamera with FOV=180. That produces a less distorted image.