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.