E. Cobham Brewer 18101897. Dictionary of Phrase and Fable. 1898.
Lath or Lathe. A division of a county. Sometimes it was an
intermediate division between a hundred and a shire, as the
lathes of Kent and rapes of Sussex, each of which contained
three or four hundreds apiece. In Ireland the arrangement was
different. The officer over a lath was called a lathreeve.
(Anglo-Saxon læth, a canton.) If all that tything failed, then
all that lath was charged for that tything; and if the lath
failed, then all that hundred was demanded for them [i.e.
turbulent fellows], and if the hundred, then the shire.Spenser:
Ireland.