not sure if this is possible, but
lava to me is hot, it needs to be cooled to become ash, to be crushed into stone
so suggest lava can't be directly made into stone,
you could use something like the existing heat transfer boiler system to turn lava into steam that powers the steam engines
it cools the lava and produces ash (spent fuel), maybe it requires water as well?
ash can then be crushed and becomes stone.
