The Collaborative International Dictionary of English v.0.48:

Counterlath \Coun"ter*lath`\, n. (Building)
   (a) A batten laid lengthwise between two rafters to afford a
       bearing for laths laid crosswise.
   (b) Any lath laid without actual measurement between two
       gauged laths.
   (c) Any of a series of laths nailed to the timbers to raise
       the sheet lathing above their surface to afford a key for
       plastering.
   (d) One of many laths used in preparing one side of a
       partition or framed wall, when the other side has been
       covered in and finished.
       [Webster 1913 Suppl.]