Their is what Marx said and whats marxists made of that. Again, this is poorly defined in Marx text and spread in a lot of them. You'd rather rely on people that study the lumpen as a context, maybe Jean-Claude Bourdin. However for orthodoxes : "From whore to pope, there is a mass of such rabble. But the honest and ‘working’ lumpenproletariat belongs here as well;" - Grundrisse