https://archive.is/S6D5o#selection-3823.0-3823.170
>they are not a real class, using this term Marx described the lowest layers of the proletariat who were most prone to petty bourg ideology due to their lack of education.
WRONG! TOTALLY UTTERLY WRONG
It was Fanon who claimed this
For Marx's conception of the lumpen proletariat one may refer to the 18th Brumaire
https://www.marxists.org/archive/marx/works/1852/18th-brumaire/ch05.htm
>This society dates from the year 1849. On the pretext of founding a benevolent society, the lumpen proletariat of Paris had been organized into secret sections, each section led by Bonapartist agents, with a Bonapartist general at the head of the whole. Alongside decayed roués with dubious means of subsistence and of dubious origin, alongside ruined and adventurous offshoots of the bourgeoisie, were vagabonds, discharged soldiers, discharged jailbirds, escaped galley slaves, swindlers, mountebanks, lazzaroni,[105] pickpockets, tricksters, gamblers, maquereaux [pimps], brothel keepers, porters, literati, organ grinders, ragpickers, knife grinders, tinkers, beggars — in short, the whole indefinite, disintegrated mass, thrown hither and thither, which the French call la bohème; from this kindred element Bonaparte formed the core of the Society of December 10. A "benevolent society" - insofar as, like Bonaparte, all its members felt the need of benefiting themselves at the expense of the laboring nation. This Bonaparte, who constitutes himself chief of the lumpenproletariat, who here alone rediscovers in mass form the interests which he personally pursues, who recognizes in this scum, offal, refuse of all classes the only class upon which he can base himself unconditionally, is the real Bonaparte, the Bonaparte sans phrase.
For a clue that it is not pauperism and destitution per se that defines the lumpen for Marx, note that he includes in its ranks among others the literati and Louis Bonaparte
Compare this to his explanation of the reserve army of labour from Das Kapital https://www.marxists.org/archive/marx/works/1867-c1/ch25.htm