Does Limecrete exist in North America?
I seriously doubt you'll find "limecrete" as a ready made product, but the lime you want (which you can then mix aggregate into) is "Mason's Lime" - unless you are abnormally brave and silly and want to risk playing with quicklime, which is VERY nasty stuff. Type S or SA (air-entraining - makes small bubbles which help various properties of the product) are probably what you want, and will be able to find at any well-stocked masonry supply.

From the second link below:


  Hydrated limes used in building applications are divided into four
  types, as described in ASTM Standard Specification C 207 (Hydrated
  Lime for Masonry Purposes): Type N – normal hydrated lime Type NA –
  normal air-entraining hydrated lime Type S – special hydrated lime
  Type SA – special air-entraining hydrated lime Types S and SA are
  differentiated from Types N and NA principally by the unhydrated oxide
  content and their water retention value. Type S must meet a water
  retention value of 85%, while Type N hydrate lime must have a water
  retention value of 75%. No distinction is made based on the nature and
  source of limestone. The maximum air content of cement-lime mortar
  made with Types NA and SA is 14%; with Types N or S lime, 7%.


Type s and sa mason's lime described.

National Lime Association

More about type S