The Collaborative International Dictionary of English v.0.48:

Lath \Lath\, n.; pl. Laths. [OE. laththe, latthe, latte, AS.
   l[ae]tta; akin to D. lat, G. latte, OHG. latta; cf. W. llath
   a rod, staff, yard. Cf. Lattice, Latten.]
   A thin, narrow strip of wood, nailed to the rafters, studs,
   or floor beams of a building, for the purpose of supporting
   the tiles, plastering, etc. A corrugated metallic strip or
   plate is sometimes used.
   [1913 Webster]

   Lath brick, a long, slender brick, used in making the floor
      on which malt is placed in the drying kiln.

   Lath nail a slender nail for fastening laths.
      [1913 Webster]

The Collaborative International Dictionary of English v.0.48:

Lath \Lath\, v. t. [imp. & p. p. Lathed; p. pr. & vb. n.
   Lathing.]
   To cover or line with laths.
   [1913 Webster]

The Collaborative International Dictionary of English v.0.48:

Lathe \Lathe\ (l[aum][th]), n. [AS. l[=ae][eth]. Of uncertain
   origin.]
   Formerly, a part or division of a county among the
   Anglo-Saxons. At present it consists of four or five
   hundreds, and is confined to the county of Kent. [Written
   also lath.] --Brande & C.
   [1913 Webster]

WordNet (r) 3.0 (2006):

lath
    n 1: a narrow thin strip of wood used as backing for plaster or
         to make latticework