Why spotlight does not work the same way with a cube (img1) and with an imported obj (img2)? Thanks.
If you are using baked lighting in your scene, the issue is most likely related to the lightmap UVs of the imported object. You can either author your UVs by hand in a 3D modeling package, or let Unity generate auto UVs for you.To do that, simply select your mesh, and in the mesh importer settings enable Generate Lightmap UVs checkbox.