[generuso]

The efficiency of X-ray tubes is proportional to voltage, and is about 1% at 100kV voltage. This is the ballpark for the garden variety Xray machines. But the wavelength of interest for lithography corresponds to the voltage of only about 100V, so the efficiency would be 10 parts per million.

The source in the ASML machine produces something like 300-500W of light. With an Xray tube this would then require an electron beam with 50 MW of power. When focused into a microscopic dot on the target this would not work for any duration of time. Even if it did, the cooling and getting rid of unwanted wavelengths would have been very difficult.

A light bulb does not work because it is not hot enough. I suppose some kind of RF driven plasma could be hot enough, but considering that the source needs to be microscopic in size for focusing reasons, it is not clear how one could focus the RF energy on it without also ruining the hardware.

So, they use a microscopic plasma discharge which is heated by the focused laser. It "only" requires a few hundred kilowatts of electricity to power and cool the source itself.