Here's how it's described by Paul Krugman in 2003, quoted by Tom Walker at Ecological Headstand:
Economists call it the "lump of labor fallacy"; It's the idea that there is a fixed amount of work to be done in the world, so any increase in the amount each worker can produce reduces the number of available jobs. (A famous example: those dire warnings in the 1950's that automation would lead to mass unemployment.) As the derisive name suggests, it's an idea economists view with contempt, yet the fallacy makes a comeback whenever the economy is sluggish.I realise that I've been guilty of this "fallacy" in running the following argument: would you/we/society rather have 100 people employed at $1,000 or 1000 people employed at $100? I thought this was a slam-dunk for both Left and Right. The Left because there are more people employed, the Right because they get cheaper labour. The only ones that would be against it would be the Unions, showing -- so I argued -- that Unions are now irrelevant and no longer working, if they ever were, for the benefit of workers in general, but only for those in employment.
There is implicit in this the lump of labour assumption, since working at fewer people working at higher wage is just another way of saying that they are doing the same amount of work at higher productivity.
But there's an argument that there is indeed a Lump of Labour, or, as Walker puts it somewhere on his blog, that "some work is lumpier that other". Indeed it would be the case for domestic workers in Hong Kong: if the base wage for them were raised, there would be fewer employed; I'm sure that would be the case -- though, to be sure, that's just a judgement with no data. So there is talk of the "lump of labour fallacy-fallacy"....
There's also the interesting offshoot of this, the Lump of Energy fallacy: the argument that if energy were cheaper we would use less of it. On the blog Crooked Timber there's some spirited discussion of this, including the so-called rebound effect, whereby it is argued that if energy were cheaper we would use more of it -- showing that there is no Lump of Energy, ie that there is a Lump of Energy fallacy.