We don't have synonyms for laithe yet — it may be a rare, specialized, newly coined, or misspelled word. The closest thesaurus entries we have are lithe, lathe and faithe.
(n) :
(Northern England) Alternative form of lathe (“A granary; a field barn”). [(obsolete) An administrative division of the county of Kent, in England, from the Anglo-Saxon period until it fell entirely out of use in the early twentieth century.]
(n) :
(Northern England) Alternative form of lathe (“A granary; a field barn”). [(obsolete) An administrative division of the county of Kent, in England, from the Anglo-Saxon period until it fell entirely out of use in the early twentieth century.]