* If you're talking about minerals: The lightest common mineral is pumice, a type of volcanic glass with a density of about 0.25 g/cm³.
* If you're talking about rocks: The lightest rock is also pumice, although some extremely porous tuff rocks can also be very light.
* If you're considering all types of solid matter: The lightest solid element is lithium, with a density of 0.534 g/cm³. It's technically not a stone, but it's the lightest solid element.
So, depending on your definition of "stone," the answer could be pumice, tuff, or lithium.