The class name must be an UpperCamelCase version of the filename with the word Controller on the end (without spaces, dashes and underscores). If the controller name is not correctly Lumberjack will not throw any errors - instead you will just get a blank page.
The handle method will automatically be called on your controller.
Changing the naming convention
If you wish to change how Lumberjack looks for controller class names, you can hook into the lumberjack_controller_name filter.