Thanks for the tips. Based on the testing I see that Shape3d and InsideOut are maybe working differently what I am looking for. I can map the image nicely with Shape3d (Sphere) but is there some way to export the rectangular map of the sphere? I would still need a rectangular map created that I could use in the Lithophane creation tool.
I would assume that the mapped output could look something like below "bend/distort" rectangular image.
I think that this is Photoshop Plugin that produces this kind of output: http://richardrosenman.com/shop/spherical-mapping-corrector/
Bend/distort Image