Language emergence is characterized by a high degree of lexical variation. It has been suggested that the speed at which lexical conventionalization occurs depends partially on social structure. In large communities, individuals receive input from many sources, creating a pressure for lexical convergence. In small, insular communities, individuals can remember idiolects and share common ground with interlocuters, allowing these communities to retain a high degree of lexical variation. We look at lexical variation in Kata Kolok, a sign language which emerged six generations ago in a Balinese village, where women tend to have more tightly-knit social networks than men. We test if there are differing degrees of lexical uniformity between women and men by reanalyzing a picture description task in Kata Kolok. We find that women’s productions exhibit less lexical uniformity than men’s. One possible explanation of this finding is that women's more tightly-knit social networks allow for remembering idiolects, alleviating the pressure for lexical convergence, but social network data from the Kata Kolok community is needed to support this explanation.