While the below web site does not provide much information about pit
style lime kilns, it is another reference to add to a bib.
 
Brief mention of pit style lime kilns is made on the Griggsville Landing
Lime Kiln page at 
 
http://www.dnr.state.il.us/orep/nrrc/cultural/cultural.htm
 
Another source to look at, although I don't recall if it discusses pit
style kilns is the following publication:
 
Rolando, Victor R.
1992     200 Years of Soot and Sweat: The History and Archeology of
Vermont's Iron, Charcoal, and Lime Industries. The Vermont
Archaeological Society. Dover Litho Printing Co., Dover, DE.
 
my best,
 
mike gregory
Great Lakes Archaeological Research Center
Milwaukee, Wisconsin