I think you only need to register the main namespace. The second parameter needs to be a path and not a file. Also try with absolute not relative path. The next problem is that your directories are lower case. So the autoloader is expecting the path LIB_FOLDER/APP/Libraries/Controller
for a namespace APP\Libraries\Controller
. I don't know if you can set aliases for converting lowercase to uppercase. But it dosn't seem so.
Try something like that:
$SPL->registerNamespace('APP', __DIR__.'/../LIB_FOLDER');