I'll invite to explore the CL ecosystem starting with https://github.com/CodyReichert/awesome-cl/ (it might be larger than one thinks)
In terms of asynchronous programming, not built-in to implementations (like, no green threads), we have
- https://github.com/orthecreedence/wookie - an asynchronous HTTP server
- https://github.com/fukamachi/woo - fast non-blocking HTTP server on top of libev.
- an actor-based task manager for Hunchentoot: https://github.com/mdbergmann/cl-tbnl-gserver-tmgr
see also https://github.com/CodyReichert/awesome-cl/#parallelism-and-... for promise libraries, async libraries, the actor library, an STM library, lparallel (run tasks in parallel, easy and often useful), bindings to other async tools.
Those libraries are active.