An enigmatic entry. Adler offers no enlightenment beyond (a) noting that there is something similar ('cf.') in the Ambrosian Lexicon, and (b) formatting the noun in the gloss as lower-case. Nevertheless, despite b, the adjective Lakaian/Lacaean is surely to be related to Lacaenian, i.e. Spartan (beta 166, lambda 47, etc.). The feminine genitive singular lakai/nhs is probably lifted bodily from its occurrence in lambda 47, immediately preceding.
The source of the headword phrase is unidentifiable.