Levenstein distance is computed as the number of elements that need to be exchanged to switch from a starting sequence to another (D_L(0010, 3000)=2). This is permutation and each exchange is atomic, so it does not even respect how close or far appart the features of the changing elements are, or whether the elements are atomic parts of speach (which they are not).
Similarity of words is investigated empiricly, for starters. I only know of one series of experiments on lexicalization in first language learning, who has found that, say peg would not be confused easily for dog depending on the context (and I'd love to name a reference work; I cannot give a qualified summary either way, especially regarding what context); whereas, I suppose, in case of impoverished context that would be most sever in aphasia, the inadvertant confusion of phonemes might be possible, I'm sure.
Yet, all that says nothing about confusion that depends on context. Lexical distance is quite something else, not precisely defined, though Word2Vec, as JK indicates above, is one famous approach leaning on distributional semantics, though slightly mechanic.