Here is the little bit of history that is available online:

Austin White Lime

As near as I can find out, these are the second set of kilns built at the plant, sometime in the late 1890s. They are to the left of the cast iron ones pictured in the link, which are circa 1920, and are also still there.

Exerior shot showing the banding with native oak and some forged iron.



Interior of the kiln, showing refactory brick manufactured by Evans & Howard of St. Louis. The Elgin brick plant, 40 miles away, was manufacturing firebrick at this time, so I have no idea why they were not used.



Detail of one of the arches below the kiln, used to remove the calcined lime. Note that this area was never tuckedpointed with a portland mortar, and although it is eroded is still structurally sound.



Veiw of another arch and removal chamber.



This photo and the following show the results of using a portland cement repair mortar over the old lime mortar (repaired in the teens, I think). All areas where the "improved" portland cement mortar were applied are deteriorating badly, with some areas in total collapse.