This paper describes a method to enrich lexical resources with content relating to linguistic diversity, based on knowledge from the field of lexical typology. We capture the phenomenon of diversity through the notion of lexical gap and use a systematic method to infer gaps semi-automatically on a large scale, which we demonstrate on the kinship domain. The resulting free diversity-aware terminological resource consists of 198 concepts, 1,911 words, and 37,370 gaps in 699 languages. We see great potential in the use of resources such as ours for the improvement of a variety of cross-lingual NLP tasks, which we illustrate through an application in the evaluation of machine translation systems.