LispyScript is not a dialect of Lisp. LispyScript is an abstraction of JavaScript. It is "Lispy" in the sense that it borrows the tree structure and use of parenthesis from Lisp.
All JavaScript data structures and functions are first class citizens of LispyScript. So all of JavaScript, and all its Libraries are available within LispyScript.
LispyScript has only one data structure of its own. That is itself! ie. LispyScript is Homoiconic. And it is homoiconic to the extreme, because there is no way to explicitly differentiate code and data in LispyScript. (In Lisp you have the "quote syntax" to explicitly differentiate code and data).
In LispyScript we differentiate code and data by context. There are special expressions in LispyScript that treat code as data. One example is the "macro" expression. (I have yet to document the others, all of them used in recursive macros. You can see them in action in the macro source for the moment).
The objective of LispyScript is "Simplicity", by abstracting away complexity, and yet remain powerful.
LispyScript has a very small core (about 400 lines of JavaScript) and the rest of LispyScript is in LispyScript itself. Also the core seems to be working very well, so I dont see any advantage in rewriting it in LispyScript.
I hope this has answered your question for the moment. I realize that I need to explain more about all this, which I hope to do in future blog posts.