Oh yea i love this contradiction cuz its never really drawn upon in the common communist discourse but it represents something interesting to me.

So im not a scholar and have only done my best, but i am not sure ive found an instance where Marx actually calls prostitutes lumpen proletariat. Marx at one point refers to Stirner’s idealist conception of lumpen proletariat in the German Ideology but is clearly making fun of Stirner’s vibes based analysis of class. Marx even cites pimps in particular as lumpenproletariat but not prostitutes in the 18th Brumaire.

As lumpe means rag the lumpen is supposed to be on an aesthetic external and superficial analysis that section of the working class so undignified under the capitalist system that they are now the outcasts of society.

Marxist classes are definitionally useful for the sole reason that they play a definite and objective role in class struggle in a historical materialist framework. Classes can therefore be defined through the lens of dialectical materialism as a definite mass of people in society who share a means of life, psychological character, and collective interest. The lumpenproletariat therefore in what i can tell are the fraction of the working class so debased as to then possess a material interest distinct from the proletariat and can even come into conflict with the proletariat. Petty thieves, robbers, beggars, drug dealers, and pimps sustain themselves on economic exploitation of other classes, which can include the proletariat.

The class interest of the lumpen pretariat can only ever politically manifest itself in what is essentially gangs. During times of revolutionary crises, the lumpenproletariat heavily benefits from the crisis of legitimacy of the state and can then more freely extort the other classes which has historically been represented in gangs that are either paid off by the bourgeois against other classes or independently of the bourgeois extort other classes whether by exacting tolls and taxes or other means. You can see the exact same thing playing out in Haiti today as Marx noted in the 18th Brumaire. Simply put, you can not “unionize” the lumpenproletariat - as a lumpenproletariat union is essentially manifest in gangs which even on a superficial level clearly represent their political interests as a class.

So from this analysis we can see that there is no “inherent revolutionary character” of the lumpenproletariat, rather only a dialectical character represented in its identity and material interest distinct from other classes. Even Marx in his own words says that the lumpenproletariat are capable of the highest forms of heroism, and the most debauched forms of hedonism. Particularly what Mao and the BPP noted is that there is a possibility to in essence develop a mass base in the lumpenproletariat and to cause a revolutionary development by the proletarianization of the people in this mass base.

In any case i hope this provides some clarity, and i hope i can be corrected on points where i am mistaken!