You can easily read Lisp code off your phone screen - it wraps around, but retains the structure. Try that trick with pretty much any non-lispy language - even "the most elegant Python" fails there, face flat.
EDN & Transit is far better than JSON - EDN is more flexible and expressive than JSON, making it a superior choice for data serialization. It's also more than two times smaller and cleaner, commas are completely optional.
Hiccup is better than JSX & HTML - far more easier, cleaner, shorter and nicer to work with.
similarly,
s-expressions are better that XML & Yaml;
CL's PLISTs and ALISTs & Clojure maps are better than Dicts/Hashes in other languages.
Basically, you can leverage the expressiveness and simplicity of Lisp-like syntax to offer structured, readable, and powerful data representations. Add to that the ability to evaluate any given form on the fly through a connected REPL, basically "trying things while you read them," and that changes everything you thought you knew about the readability of code.
Those who call Lisp "non-readable" I suppose, in fact, never tried to actually read it. Of course, if you never learn a language, it would remain incomprehensible.