I'm curious too. From the website[0] it looks like Egison was designed to do pattern matching. The whole language is built around it. This way Egison can do more complicated kinds of pattern matching such as matching patterns against graphs or other complicated data structures. I don't see why any of these features could not be added to an existing Lisp. OTOH, it might not be about adding more features, it might be about doing it efficiently. If that is the case creating a new language is almost a requirement.
[0] http://www.egison.org/faq.html