In order to describe electric pottery kilns sometimes people list them as Sitter LT-3K but this is always incorrect.   The Kiln Sitter is a mechanical devise attached to the side of a kiln and it disconnects power from the heating elements when the cone temperature inside is achieved.  It is a standard item on kilns made without electronic control devises.  It does not identify the kiln or tell anything about the kiln itself.  Many of them are made by Dawson.
When people purchase a kiln they generally want to know the manufacturer such as Skutt, L&L, Evenheat, Crusader or Amaco.  People want to know the temperature that a kiln can reach and the power it will draw.  This should be on a small plaque attached to the side of the kiln itself.  The other concern is the interior dimension of the kiln and often this is contained in the model number.  If not, just measure inside width and height.