By using a distance-based subgrouping method the Levenshtein is susceptible to exactly the same problems that classical lexicostatistics faced (Swadesh 1952).
the correct classification of triplets is the simplest possible subgrouping task, with only four possible subgroupings: language A is more similar to language B than C (A,B|C), A is closer to C (A,C|B), B is closer to C (B,C|A), and no language is closer to the other (A,B,C).