It is a slimmed down, modernized fork of Slime. Slime works across all Common Lisp implementations. Sly takes advantage of improvements to Emacs Elisp implemented in Emacs 24.3 and higher. So it looks like it is not tied to any particular Common Lisp implementation, but you need to use a modern Emacs.
Modern is a relative term. 24.3 was released in 2013!