.stl files aren't like .obj files because they cannot contain information about normals, don't use triangle indexing and cannot contain information about UVs.

You can use Meshlab to convert .stl files to .obj. On import of the .stl mesh file into Meshlab you'll be asked whether you wish to merge duplicate vertices. You'd want to choose yes because .stl doesn't use vertex indexing and each triangle is basically regarded as separate and on its own. And every vertex is consequently duplicated for each triangle that has a point at that vertex. Then you would go to Filters => 'Normals, Curvatures and Orientation' => 'Re-Compute Vertex Normals'. Then you can export as an .obj from File => 'Export Mesh As'.

You can also just use Meshmixer to open the .stl file and export as .obj. It should automatically attempt to generate averaged vertex normals, from my experience.