Lexical similarity data, quantifying the "proximity" of languages based on the similarity of their lexicons, has been increasingly used to estimate the cross-lingual reusability of language resources, for tasks such as bilingual lexicon induction or cross-lingual transfer. Existing similarity data, however, originates from the field of comparative linguistics, computed from very small expert-curated vocabularies that are not supposed to be representative of modern lexicons. We explore a different, fully automated approach to lexical similarity computation, based on an existing 8-million-entry cognate database created from online lexicons orders of magnitude larger than the word lists typically used in linguistics. We compare our results to earlier efforts, and automatically produce intuitive visualizations that have traditionally been hand-crafted. With a new, freely available database of over 27 thousand language pairs over 331 languages, we hope to provide more relevant data to cross-lingual NLP applications, as well as material for the synchronic study of contemporary lexicons.