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

Moby Thesaurus II by Grady Ward, 1.0:

107 Moby Thesaurus words for "lath":
   Mystik tape, Scotch tape, adhesive tape, band, bandage, batten,
   beam, belt, billet, board, boarding, brick, cellophane tape,
   clapboard, cloth tape, cord, cordwood, deal, driftwood, face,
   fascia, fillet, firewood, friction tape, girdle, glass, glaze,
   gruel, hardwood, lathing, lathwork, ligula, ligule, list, log,
   lumber, masking tape, mere shadow, panelboard, paneling, panelwork,
   paper, plank, planking, plastic tape, plyboard, plywood, pole,
   post, puncheon, rail, rake, revet, ribband, ribbon, shadow, shake,
   shaving, sheathe, sheathing, sheathing board, sheeting, shingle,
   shred, sideboard, siding, skeleton, slab, slat, slate, slip,
   softwood, soup, spill, splat, spline, splinter, stave, stick,
   stick of wood, stone, stovewood, strake, strap, streak, strip,
   strop, taenia, tape, tape measure, tapeline, thatch, three-by-four,
   ticker tape, tile, timber, timbering, timberwork, two-by-four,
   vein, veneer, wafer, wall in, wall up, wallpaper, weatherboard,
   wood