zlib or libz is a well known compression library. It has several lisp implementations and FFI's:
The newest (C)FFI based one supporting its streaming interface is here
in the cl-quasi-quote repo.
ZLIB is a purely Common Lisp implementation of the zlib CompressionLibrary. It was originally written by Harald Musum and is now maintained by Matthieu Villeneuve. It is licensed under the LLGPL.