Calling something a fallacy does not mean it truly is one. I have not seen strong evidence that there is not a "lump of labor" in extremely high-rent countries like the US.
For a sufficiently small period of time, there absolutely is a "lump of labor". If I were to go into a county with robots and rent them out to employers for 1/4 of the wage of their current employees, and they all fired their employees and accepted my robots, do you really believe that all of ex-employees would be able to find work again within 6 months? Or even 70% of them? What about their new wages? Do you think these new jobs would pay as well? I have a hard time believing that to be the case.
There are a number of misconceptions when it comes to the lump of labor fallacy. The prevalent one is confusing the small and the big picture.
If a factory introduces automation, no doubt that the resulting job losses are a problem that must be addressed.
However, the lump of labor refers to the big picture - in the same time span, other jobs are created elsewhere. If they weren't, considering that automation started at least 200 years ago (in the most limited sense of the term), the whole planet would be out of jobs by now.
For a sufficiently small period of time, there absolutely is a "lump of labor". If I were to go into a county with robots and rent them out to employers for 1/4 of the wage of their current employees, and they all fired their employees and accepted my robots, do you really believe that all of ex-employees would be able to find work again within 6 months? Or even 70% of them? What about their new wages? Do you think these new jobs would pay as well? I have a hard time believing that to be the case.