Please provide a full phrase (or even a paragraph) in such questions. Normally it is impossible to translate one word without a context.

Depending on context "лакейскую" can be either adjective in feminine form, Accusative case or adjectival noun in Accusative case.

If adjective, "лакейская" can mean, for example "servile". If noun, it means "the room downstairs" that is the room in noble house where servants reside.