from
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.]