Hot rock cooking - type of rock required
For hot rock cooking, you want four properties of the stone:


A smooth, non-porous surface.
This is almost (ok, at least a bit) like a non-stick surface and means you can clean it afterwards. Neither food nor detergent should "seep into" the stone.
High thermal mass.
You want to make sure that your stone is not significantly cooled down by your food as this would interrupt your cooking process and increase the likelihood of the food sticking to the stone.
Relatively resistant to temperature change.
During its use, a hot stone will be repeatedly heated up and cool down again. This can cause small cracks or unevennesses to widen and destroy the material.
Food safety.
The absence of toxic minerals that could leech into the food. Probably a pretty self-evident point.


I can not answer this for the volcanic rocks you can get your hands on, although some like pumice are obviously out. But I'm not a geologist. Note that a standard hot rock material would be granite. If your candidate fulfills the four criteria above, go for it.