As @orekelens states in the comments, and confirmed also by Free Dictionary, Lymphatic is an archaic word for
Lacking energy or vitality; sluggish.
The origin of the word comes from
1640s, from Modern Latin lymphaticus "pertaining to the lymph," from Latin lympha (see lymph). The English word also sometimes is used in what was the primary sense of lymphaticus in classical Latin, "mad, frenzied." OED reports this meaning "difficult to account for," but perhaps due to association of lympha with nymphe; compare Greek nymphian "to be frenzy-stricken." Also sometimes in reference to the appearance or temperament of one thought to suffer from excess of lymph, "dull, sluggish, slow in thought or action, with flabby muscles and pale skin" (1834).
Schmoop talks about the passage quoted from The Invisible Man by saying
Here, Mrs. Hall wants Millie to speed up her work. How does she do this?: "by a few deftly chosen expressions of contempt."