The OBJ exports are fine and render perfectly for me, you are probably removing normals either on import or with an operation/modifier in Max.
There's a difference in how surface normals are created in CAD apps vs Max.
In CAD, the surface curvature is typically perfectly described by mathematical functions (yeah, super simplistic way to put it) and for mesh display/rendering, the surface is tesselated, with each triangle/polygon getting a surface normal derived from these functions which is very accurate and independent from mesh resolution. The result is that, even for coarse tessellation, the surface curvature looks good. This is called 'explicit normals' in Max and you should always try to keep them when importing CAD meshes into Max.
In Max, the concept of smoothing means that surface normals are calculated by averaging the face/polygon vertices which is heavily dependent on the tessellation and will be worse than what CAD apps are doing, especially with triangulated meshes (quad meshes are better suited for this).
It looks like you are not importing explicit normals correctly, or removing/invalidating them in Max. Various modifiers will invalidate explicit normals on imported CAD meshes, so will space warps, Booleans (or attaching/detaching mesh elements in earlier Max versions). Once invalidated, Max will fall back to using smoothing groups which will not look well on triangulated meshes, this is what's happening here.
On OBJ import make sure, that in the dialog's 'Normals' section 'Import from file' is enabled.
To check if a CAD imported object has correct normals in Max, use an 'Edit normals' modifier on the object - if it displays green normals, you've imported and kept them, and the object will render fine. If they're blue, it means you have either not imported them correctly, or some operation/modifier has removed them. Unfortunately, there's no way to get them back in Max without re-importing the object.
You may be facing a different issue with CAD meshes further down the road where the shadow terminator may look jagged (with non-transparent materials). This is due to the way Corona handles lighting vs surface normals. Let us know if you see this, there's a way to fix it but it may not be satisfactory. But it's unrelated to the issue you've been running into.