You can check my iPhone render in the gallery (C4D Corona).. I have used HDR lightning only.
I have set it up like I would do normally. Create Sky object, create Corona Material. In Corona Material assign HDR map to diffuse slot and make sure it is a spherical projection. Apply the map to Sky object. Tweak Exposure or Offset of the bitmap as you need.
I am not sure that this is the right way to do it, but it works :)
I have also tried with Emission slot instead of diffuse, in corona material, but it doesn't work. Neither it works with standard c4d material and luminance channel.
Maybe we can get some official answers here.