Lumpenproletariat and Productivity

The prototype of Marx's concept of Labor is manufacturing, a transforming of some given material that, by virtue of having a yield, can be characterized as 'productive'.  Now, these concepts of Labor and Productivity can be extended to other kinds of work, e. g. the arrival of food is the product of the labor of a waiter, and the improved condition of a patient is the product of the labor of a physician.  But, then, so, too are the applicable to the pleasure that is the result of the efforts of an organ-grinder, or of those of a prostitute.  So, Non-Productivity is not the adequate criterion for the categorization of the latter two as Lumpenproletarian as Marx takes it to be.