The question is whether it is physically possible to build a laser using only the photoelectric effect in the vacuum, with no lasing material.
I know that there is a whole history of laser development in which people found all sorts of materials that lase if you pump them hard enough, but my question is simpler and more fundamental. Is it really necessary to have a lasing material in order to have a laser?
There already exists a patented optical amplifier using the photoelectric effect in the vacuum, and so I think it should be possible to build a laser, which is basically an optical amplifier between two mirrors. The advantage of such a photoelectric-effect laser is that the applied voltage would allow you to smoothly vary the color of the light produced, instead of relying on a pre-existing electronic-state transition in your gas molecules or a fixed energy band gap in your semiconductor material.