Term used by Karl Marx and Friedrich Engels to describe members of the most destitute of social classes in society. As criminals, sex workers, beggars, vagrants, the unemployed and other dispossessed characters who are outside the normal wage-labour system, they do not have the class consciousness necessary to organise themselves into pressing the bourgeoise for better conditions. Instead, they would rely on the bourgeoise and aristocracy for patronage, a reliance that would make them support the status-quo and potentially become a reactionary force. Marx and Engels adopted the term to describe people in the historical working class who simply do not behave in the best interests of their own class because of personal circumstances (they are tied to the bottle, or reckon that crime does pay).
In high German the word 'lumpen' means 'rags', the garment of habit by members of the Lumpenproletariat in Marx's times.
The words academic Lumpenproletariat and Lumpenprofessoriat show that the term has survived, if in tongue-in-cheek useage, to describe how through casualisation of the labour force some professionals like teachers are no longer able to collectively unite and fight for better working conditions. I expect the word Lumpenprogrammeriat to surface soon.